UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM N-Q

       QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
                               INVESTMENT COMPANY

                  Investment Company Act file number 811-22528
                                                    -----------

                     First Trust Energy Infrastructure Fund
        ----------------------------------------------------------------
               (Exact name of registrant as specified in charter)

                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
        ----------------------------------------------------------------
              (Address of principal executive offices) (Zip code)

                             W. Scott Jardine, Esq.

                          First Trust Portfolios L.P.
                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
        ----------------------------------------------------------------
                    (Name and address of agent for service)

        Registrant's telephone number, including area code: 630-765-8000
                                                           --------------

                      Date of fiscal year end: November 30
                                              -------------

                   Date of reporting period: August 31, 2014
                                            -----------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q unless the
Form displays a currently valid Office of Management and Budget ("OMB") control
number. Please direct comments concerning the accuracy of the information
collection burden estimate and any suggestions for reducing the burden to the
Secretary, Securities and Exchange Commission, 100 F Street, NE, Washington, DC
20549. The OMB has reviewed this collection of information under the clearance
requirements of 44 U.S.C. ss. 3507.





ITEM 1. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.

FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS
AUGUST 31, 2014 (UNAUDITED)



     SHARES                                     DESCRIPTION                                    VALUE
---------------  --------------------------------------------------------------------      --------------
                                                                                     
COMMON STOCKS - 95.6%

                 ELECTRIC UTILITIES - 20.4%
         163,400 American Electric Power Co., Inc. (a)...............................      $    8,774,580
          28,200 Duke Energy Corp. ..................................................           2,086,518
         160,400 Emera, Inc. (CAD) (a)...............................................           5,071,785
         176,800 Fortis, Inc. (CAD) (a)..............................................           5,450,507
          62,000 IDACORP, Inc. (a)...................................................           3,516,640
         255,800 ITC Holdings Corp. (a)..............................................           9,554,130
         200,300 NextEra Energy, Inc. (a)............................................          19,719,535
         396,600 Northeast Utilities (a).............................................          18,199,974
         132,400 NRG Yield, Inc., Class A (a)........................................           7,201,236
         459,900 Southern (The) Co. (a)..............................................          20,419,560
                                                                                           --------------
                                                                                               99,994,465
                                                                                           --------------

                 GAS UTILITIES - 8.7%
         111,800 Atmos Energy Corp. (a)..............................................           5,652,608
          61,385 Laclede Group, Inc. ................................................           3,035,488
         154,000 One Gas, Inc. (a)...................................................           5,764,220
         225,000 Questar Corp. ......................................................           5,289,750
          59,000 South Jersey Industries, Inc. ......................................           3,419,050
         367,479 UGI Corp. (a).......................................................          19,469,038
                                                                                           --------------
                                                                                               42,630,154
                                                                                           --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 0.3%
          47,000 Pattern Energy Group, Inc. .........................................           1,515,045
                                                                                           --------------

                 MULTI-UTILITIES - 16.4%
          49,000 Alliant Energy Corp. (a)............................................           2,866,010
         104,200 ATCO, Ltd., Class I (CAD) (a).......................................           4,484,060
         166,000 Canadian Utilities, Ltd., Class A (CAD) (a).........................           5,975,572
         286,000 CMS Energy Corp. (a)................................................           8,734,440
         221,900 Dominion Resources, Inc. (a)........................................          15,581,818
         107,000 National Grid PLC, ADR (a)..........................................           7,997,180
         145,000 NiSource, Inc. .....................................................           5,752,150
         133,000 Public Service Enterprise Group, Inc. ..............................           4,972,870
         142,000 SCANA Corp. ........................................................           7,375,480
          59,000 Sempra Energy (a)...................................................           6,252,230
         235,100 Wisconsin Energy Corp. (a)..........................................          10,657,083
                                                                                           --------------
                                                                                               80,648,893
                                                                                           --------------

                 OIL, GAS & CONSUMABLE FUELS - 49.8%
       1,589,216 Enbridge Energy Management, LLC (a) (b).............................          56,925,717
         458,600 Enbridge Income Fund Holdings, Inc. (CAD) (a).......................          13,631,888
         234,169 Enbridge, Inc. (a)..................................................          11,673,325
         417,000 Inter Pipeline, Ltd. (CAD) (a)......................................          13,914,062
          40,300 Keyera Corp. (CAD) (a)..............................................           3,545,570
         577,966 Kinder Morgan Management, LLC (a) (b)...............................          56,478,838
         630,500 Kinder Morgan, Inc. (a).............................................          25,383,930
         133,100 Pembina Pipeline Corp. (CAD) (a)....................................           6,116,993
         399,400 Spectra Energy Corp. (a)............................................          16,639,004
         223,500 TransCanada Corp. (a)...............................................          12,019,830



                See Notes to Quarterly Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2014 (UNAUDITED)



     SHARES/
      UNITS                                  DESCRIPTION                                       VALUE
---------------  --------------------------------------------------------------------      --------------
                                                                                     
COMMON STOCKS (CONTINUED)

                 OIL, GAS & CONSUMABLE FUELS (CONTINUED)
         476,700 Williams (The) Cos., Inc. (a).......................................      $   28,335,048
                                                                                           --------------
                                                                                              244,664,205
                                                                                           --------------
                 TOTAL COMMON STOCKS ................................................         469,452,762
                 (Cost $382,124,601)                                                       --------------

MASTER LIMITED PARTNERSHIPS - 30.9%

                 GAS UTILITIES - 2.3%
         189,764 AmeriGas Partners, L.P. (a).........................................           8,780,380
          60,000 Suburban Propane Partners, L.P. (a).................................           2,668,200
                                                                                           --------------
                                                                                               11,448,580
                                                                                           --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 0.3%
          39,300 NextEra Energy Partners, L.P. (c)...................................           1,379,823
                                                                                           --------------

                 OIL, GAS & CONSUMABLE FUELS - 28.3%
          24,000 Access Midstream Partners, L.P. (a).................................           1,544,400
          44,000 Alliance Holdings GP, L.P. (a)......................................           3,160,080
         265,430 Alliance Resource Partners, L.P. (a)................................          13,207,797
         255,200 El Paso Pipeline Partners, L.P. (a).................................          10,606,112
         117,000 Energy Transfer Equity, L.P. (a)....................................           7,096,050
         151,400 Energy Transfer Partners, L.P. (a)..................................           8,697,930
         229,200 Enterprise Products Partners, L.P. (a)..............................           9,312,396
          73,700 EQT Midstream Partners, L.P. (a)....................................           7,185,013
         218,876 Holly Energy Partners, L.P. (a).....................................           7,943,010
          75,600 Magellan Midstream Partners, L.P. (a)...............................           6,345,108
         120,239 Natural Resource Partners, L.P. (a).................................           1,909,395
         103,472 NGL Energy Partners, L.P. (a).......................................           4,405,838
         164,200 ONEOK Partners, L.P. (a)............................................           9,758,406
           8,100 Phillips 66 Partners, L.P. (a)......................................             599,400
         126,686 Plains All American Pipeline, L.P. (a)..............................           7,592,292
         156,500 Spectra Energy Partners, L.P. (a)...................................           8,918,935
         162,095 TC Pipelines, L.P. (a)..............................................           9,502,009
         249,628 Teekay LNG Partners, L.P. (a).......................................          10,833,855
         172,762 TransMontaigne Partners, L.P. (a)...................................           7,601,528
          50,000 Williams Partners, L.P. (a).........................................           2,650,500
                                                                                           --------------
                                                                                              138,870,054
                                                                                           --------------
                 TOTAL MASTER LIMITED PARTNERSHIPS ..................................         151,698,457
                 (Cost $102,370,028)                                                       --------------

                 TOTAL INVESTMENTS - 126.5% .........................................         621,151,219
                 (Cost $484,494,629) (d)                                                   --------------

   NUMBER OF
   CONTRACTS                                    DESCRIPTION                                    VALUE
---------------  --------------------------------------------------------------------      --------------

CALL OPTIONS WRITTEN - (0.4%)

                 American Electric Power Co., Inc. Calls
             100 @   $55.00 due November 2014........................................              (8,000)
             800 @    60.00 due January 2015.........................................             (16,000)
                                                                                           --------------
                                                                                                  (24,000)
                                                                                           --------------



                See Notes to Quarterly Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2014 (UNAUDITED)



   NUMBER OF
   CONTRACTS                                    DESCRIPTION                                    VALUE
---------------  --------------------------------------------------------------------      --------------
                                                                                     
CALL OPTIONS WRITTEN (CONTINUED)

                 CMS Energy Corp. Calls
           1,400 @   $32.50 due September 2014.......................................      $       (3,577)
             300 @    30.00 due December 2014........................................             (33,600)
                                                                                           --------------
                                                                                                  (37,177)
                                                                                           --------------
                 Dominion Resources, Inc. Calls
             700 @    72.50 due October 2014.........................................             (24,500)
             630 @    75.00 due January 2015.........................................             (37,800)
                                                                                           --------------
                                                                                                  (62,300)
                                                                                           --------------
                 Duke Energy Corp. Call
             100 @    75.00 due September 2014.......................................              (3,500)
                                                                                           --------------
                 Enbridge, Inc. Call
           1,516 @    50.00 due January 2015.........................................            (274,396)
                                                                                           --------------
                 IDACORP, Inc. Call
             120 @    60.00 due November 2014........................................              (2,700)
                                                                                           --------------
                 Kinder Morgan, Inc. Calls
             800 @    40.00 due September 2014.......................................             (65,600)
             200 @    37.50 due December 2014........................................             (64,800)
           1,500 @    40.00 due December 2014........................................            (238,500)
           1,000 @    45.00 due December 2014........................................             (19,500)
             300 @    40.00 due March 2015...........................................             (57,600)
                                                                                           --------------
                                                                                                 (446,000)
                                                                                           --------------
                 National Grid PLC Calls
             250 @    75.00 due September 2014.......................................             (15,625)
             330 @    80.00 due December 2014........................................             (12,375)
                                                                                           --------------
                                                                                                  (28,000)
                                                                                           --------------
                 Nextera Energy, Inc. Call
           1,480 @    105.00 due September 2014......................................             (14,800)
                                                                                           --------------
                 NiSource, Inc. Calls
           1,300 @    41.00 due October 2014.........................................             (65,000)
             150 @    42.00 due January 2015.........................................             (13,500)
                                                                                           --------------
                                                                                                  (78,500)
                                                                                           --------------
                 Northeast Utilities Calls
             110 @    45.00 due October 2014.........................................             (12,100)
           2,260 @    50.00 due October 2014.........................................             (22,600)
                                                                                           --------------
                                                                                                  (34,700)
                                                                                           --------------
                 One Gas, Inc. Call
             540 @    40.00 due October 2014.........................................             (48,600)
                                                                                           --------------
                 Plains All American Pipeline, L.P. Calls
             100 @    60.00 due October 2014.........................................             (14,000)
             380 @    60.00 due November 2014........................................             (64,600)



                See Notes to Quarterly Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2014 (UNAUDITED)



   NUMBER OF
   CONTRACTS                                    DESCRIPTION                                    VALUE
---------------  --------------------------------------------------------------------      --------------
                                                                                     
CALL OPTIONS WRITTEN (CONTINUED)

                 Plains All American Pipeline, L.P. Calls
                 (Continued)
             370 @   $62.50 due November 2014........................................      $      (20,720)
                                                                                           --------------
                                                                                                  (99,320)
                                                                                           --------------
                 Public Service Enterprise Group, Inc. Call
             600 @    45.00 due December 2014........................................             (15,000)
                                                                                           --------------
                 Questar Corp. Call
           1,350 @    25.00 due January 2015.........................................             (37,125)
                                                                                           --------------
                 SCANA Corp. Calls
             650 @    55.00 due November 2014........................................             (13,000)
             200 @    55.00 due February 2015........................................             (11,600)
                                                                                           --------------
                                                                                                  (24,600)
                                                                                           --------------
                 Sempra Energy Call
             300 @    105.00 due September 2014......................................             (51,000)
                                                                                           --------------
                 Southern (The) Co. Calls
           1,150 @    45.00 due November 2014........................................             (78,200)
           1,600 @    47.00 due November 2014........................................             (25,600)
                                                                                           --------------
                                                                                                 (103,800)
                                                                                           --------------
                 Spectra Energy Corp. Calls
             210 @    39.00 due September 2014.......................................             (55,125)
           2,180 @    43.00 due September 2014.......................................             (28,340)
                                                                                           --------------
                                                                                                  (83,465)
                                                                                           --------------
                 TransCanada Corp. Call
             730 @    50.00 due November 2014........................................            (306,600)
                                                                                           --------------
                 UGI Corp. Call
           2,070 @    55.00 due January 2015.........................................            (155,250)
                                                                                           --------------
                 Williams (The) Cos., Inc. Calls
           1,700 @    60.00 due October 2014.........................................            (170,000)
           1,160 @    62.50 due October 2014.........................................             (39,440)
                                                                                           --------------
                                                                                                 (209,440)
                                                                                           --------------
                 Wisconsin Energy Corp. Call
           1,390 @    50.00 due January 2015.........................................             (27,800)
                                                                                           --------------
                 TOTAL CALL OPTIONS WRITTEN .........................................          (2,168,073)
                 (Premiums received $1,838,242)                                            --------------

                 OUTSTANDING LOAN - (29.7%) .........................................        (145,900,000)

                 NET OTHER ASSETS AND LIABILITIES - 3.6% ............................          17,879,047
                                                                                           --------------
                 NET ASSETS - 100.0% ................................................      $  490,962,193
                                                                                           ==============



                See Notes to Quarterly Portfolio of Investments





FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
AUGUST 31, 2014 (UNAUDITED)

----------------------------

      (a)   All or a portion of this security serves as collateral on the
            outstanding loan.

      (b)   Non-income producing security which pays in-kind distributions. For
            the fiscal year to date period (December 1, 2013 through August 31,
            2014), the Fund received 82,632 shares of Enbridge Energy
            Management, LLC and 30,081 shares of Kinder Morgan Management, LLC.

      (c)   Non-income producing security.

      (d)   Aggregate cost for financial reporting purposes, which approximates
            the aggregate cost for federal income tax purposes. As of August 31,
            2014, the aggregate gross unrealized appreciation for all securities
            in which there was an excess of value over tax cost was $138,483,648
            and the aggregate gross unrealized depreciation for all securities
            in which there was an excess of tax cost over value was $1,827,058.

      ADR   American Depositary Receipt

      CAD   Canadian Dollar - Security is denominated in Canadian Dollars and is
            translated into U.S. Dollars based upon the current exchange rate.

INTEREST RATE SWAP AGREEMENTS:


                                                               NOTIONAL
     COUNTERPARTY      FLOATING RATE(1)   EXPIRATION DATE       AMOUNT      FIXED RATE(1)       VALUE
---------------------------------------------------------------------------------------------------------
                                                                             
Bank of Nova Scotia    1 month LIBOR          10/08/20      $   36,475,000     2.121%        $ (637,183)
Bank of Nova Scotia    1 month LIBOR          09/03/24          36,475,000     2.367%           (18,932)
                                                            --------------                  -------------
                                                            $   72,950,000                  $  (656,115)
                                                            ==============                  =============



(1)   The Fund pays the fixed rate and receives the floating rate. The floating
      rate on August 31, 2014 was 0.159%.

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of August 31,
2014 is as follows (see Note 2A - Portfolio Valuation in the Notes to Quarterly
Portfolio of Investments):



                                                  ASSETS TABLE
                                                                                      LEVEL 2          LEVEL 3
                                                     TOTAL                          SIGNIFICANT      SIGNIFICANT
                                                    VALUE AT      LEVEL 1 QUOTED     OBSERVABLE      UNOBSERVABLE
                                                   8/31/2014          PRICES           INPUTS           INPUTS
                                                ---------------- ---------------- ---------------- ----------------
                                                                                       

Common Stocks*................................. $   469,452,762  $   469,452,762  $            --  $             --
Master Limited Partnerships *..................     151,698,457      151,698,457               --                --
                                                ---------------- ---------------- ---------------- ----------------
TOTAL ......................................... $   621,151,219  $   621,151,219  $            --  $             --
                                                ================ ================ ================ ================

                                               LIABILITIES TABLE

                                                     TOTAL                          SIGNIFICANT      SIGNIFICANT
                                                    VALUE AT     LEVEL 1 QUOTED      OBSERVABLE      UNOBSERVABLE
                                                   8/31/2014         PRICES            INPUTS           INPUTS
                                                ---------------- ---------------- ---------------- ----------------
Call Options Written........................... $    (2,168,073) $    (2,168,073) $            --  $            --
Interest Rate Swaps** .........................        (656,115)              --         (656,115)              --
                                                ---------------- ---------------- ---------------- ----------------
TOTAL ......................................... $    (2,824,188) $    (2,168,073) $      (656,115) $            --
                                                ================ ================ ================ ================


*  See Portfolio of Investments for industry breakout.
** See Interest Rate Swap Agreements for contract detail.

All  transfers  in  and  out  of  the Levels during the period are assumed to be
transferred  on the last day of the period at their current value. There were no
transfers between Levels at August 31, 2014.


                See Notes to Quarterly Portfolio of Investments





NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS


                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2014 (UNAUDITED)


                                1. ORGANIZATION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011 and is registered with the Securities and Exchange
Commission under the Investment Company Act of 1940, as amended (the "1940
Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").


                     2. VALUATION AND INVESTMENT PRACTICES

A. PORTFOLIO VALUATION:

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. Foreign securities are
priced using data reflecting the earlier closing of the principal markets for
those securities. The NAV per Common Share is calculated by dividing the value
of all assets of the Fund (including accrued interest and dividends), less all
liabilities (including accrued expenses, dividends declared but unpaid and any
borrowings of the Fund) by the total number of Common Shares outstanding.

The Fund's investments are valued daily at market value or, in absence of market
value with respect to any portfolio securities, at fair value. Market value
prices represent last sale or official closing prices from a national or foreign
exchange (i.e. a regulated market) and are primarily obtained from third party
pricing services. Fair value prices represent any prices not considered market
value prices and are either obtained from a third party pricing service or are
determined by First Trust Advisors L.P.'s (the "Advisor") Pricing Committee in
accordance with valuation procedures adopted by the Fund's Board of Trustees,
and in accordance with provisions of the 1940 Act. Investments valued by the
Advisor's Pricing Committee are footnoted as such in the footnotes to the
Portfolio of Investments. The Fund's investments are valued as follows:

      Common stocks, master limited partnerships ("MLPs") and other equity
      securities listed on any national or foreign exchange (excluding The
      NASDAQ(R) Stock Market, LLC ("NASDAQ") and the London Stock Exchange
      Alternative Investment Market ("AIM")) are valued at the last sale price
      on the exchange on which they are principally traded, or for NASDAQ and
      AIM securities, the official closing price. Securities traded on more than
      one securities exchange are valued at the last sale price or official
      closing price, as applicable, at the close of the securities exchange
      representing the principal market for such securities.

      Exchange-traded options contracts are valued at the closing price in the
      market where such contracts are principally traded. If no closing price is
      available, exchange-traded options contracts are fair valued at the mean
      of their most recent bid and asked price, if available, and otherwise at
      their closing bid price. Over-the-counter options contracts are fair
      valued at the mean of their most recent bid and asked price, if available,
      and otherwise at their closing bid price.

      Securities traded in an over-the-counter market are fair valued at the
      mean of their most recent bid and asked price, if available, and otherwise
      at the closing bid price.

      Swaps are valued utilizing quotations provided by a third party pricing
      service or, if the pricing service does not provide a value, by quotes
      provided by the selling dealer or financial institution.

      Short-term investments that mature in less than 60 days when purchased are
      fair valued at amortized cost.

Certain securities may not be able to be priced by pre-established pricing
methods. Such securities may be valued by the Fund's Board of Trustees or its
delegate at fair value. These securities generally include, but are not limited
to, restricted securities (securities which may not be publicly sold without
registration under the Securities Act of 1933, as amended) for which a pricing
service is unable to provide a market price; securities whose trading has been
formally suspended; a security whose market or fair value price is not available
from a pre-established pricing source; a security with respect to which an event
has occurred that is likely to materially affect the value of the security after
the market has closed but before the calculation of the Fund's NAV or make it
difficult or impossible to obtain a reliable market quotation; and a security
whose price, as provided by the pricing service, does not reflect the security's
"fair value." As a general principle, the current "fair value" of a security
would appear to be the amount which the owner might reasonably expect to receive
for the security upon its current sale. When fair value prices are used,
generally they will differ from market quotations or official closing prices on
the applicable exchanges. A variety of factors may be considered in determining
the fair value of such securities, including, but not limited to, the following:

      1)  the type of security;

      2)  the size of the holding;

      3)  the initial cost of the security;

      4)  transactions in comparable securities;

      5)  price quotes from dealers and/or pricing services;

      6)  relationships among various securities;





NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (Continued)


                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2014 (UNAUDITED)


      7)  information obtained by contacting the issuer, analysts, or the
          appropriate stock exchange;

      8)  an analysis of the issuer's financial statements; and

      9)  the existence of merger proposals or tender offers that might affect
          the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

      1)  the value of similar foreign securities traded on other foreign
          markets;

      2)  ADR trading of similar securities;

      3)  closed-end fund trading of similar securities;

      4)  foreign currency exchange activity;

      5)  the trading prices of financial products that are tied to baskets of
          foreign securities;

      6)  factors relating to the event that precipitated the pricing problem;

      7)  whether the event is likely to recur; and

      8)  whether the effects of the event are isolated or whether they affect
          entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

      o   Level 1 - Level 1 inputs are quoted prices in active markets for
          identical investments. An active market is a market in which
          transactions for the investment occur with sufficient frequency and
          volume to provide pricing information on an ongoing basis.

      o   Level 2 - Level 2 inputs are observable inputs, either directly or
          indirectly, and include the following:

          o   Quoted prices for similar investments in active markets.

          o   Quoted prices for identical or similar investments in markets that
              are non-active. A non-active market is a market where there are
              few transactions for the investment, the prices are not current,
              or price quotations vary substantially either over time or among
              market makers, or in which little information is released
              publicly.

          o   Inputs other than quoted prices that are observable for the
              investment (for example, interest rates and yield curves
              observable at commonly quoted intervals, volatilities, prepayment
              speeds, loss severities, credit risks, and default rates).

          o   Inputs that are derived principally from or corroborated by
              observable market data by correlation or other means.

      o   Level 3 - Level 3 inputs are unobservable inputs. Unobservable inputs
          may reflect the reporting entity's own assumptions about the
          assumptions that market participants would use in pricing the
          investment.

The inputs or methodology used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of August 31, 2014, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS:

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock and MLPs held in the Fund's portfolio as determined to be
appropriate by Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"). The
number of options the Fund can write (sell) is limited by the amount of common
stock and MLPs the Fund holds in its portfolio. The Fund will not write (sell)
"naked" or uncovered options. Options are marked-to-market daily and their value
will be affected by changes in the value and dividend rates of the underlying
equity securities, changes in interest rates, changes in the actual or perceived
volatility of the securities markets and the underlying equity securities and
the remaining time to the options' expiration. The value of options may also be
adversely affected if the market for the options becomes less liquid or trading
volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying security
exceeds the option's exercise price, it is likely that the option holder will
exercise the option. If an option written (sold) by the Fund is exercised, the
Fund would be obligated to deliver the underlying security to the option holder
upon payment of the strike price. In this case, the option premium received by
the Fund will be added to the amount realized on the sale of the underlying
security for purposes of determining gain or loss. If the price of the
underlying security is less than the option's strike price, the option will
likely expire without being exercised. The option premium received by the Fund
will, in this case, be treated as short-term capital gain on the expiration date
of the option. The Fund may also elect to close out its position in an option
prior to its expiration by purchasing an option of the same series as the option
written (sold) by the Fund.

The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at





NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (CONTINUED)


                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2014 (UNAUDITED)


inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security
covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Over-the-counter options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SWAP AGREEMENTS:

The Fund may enter into total return equity swap and interest rate swap
agreements. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed upon prices, rates,
etc. Swap agreements are individually negotiated and involve the risk of the
potential inability of the Counterparties to meet the terms of the agreement. In
connection with these agreements, cash and securities may be identified as
collateral in accordance with the terms of the respective swap agreements to
provide assets of value and recourse in the event of default under the swap
agreement or bankruptcy/insolvency of a party to the swap agreement. In the
event of a default by the Counterparty, the Fund will seek withdrawal of this
collateral and may incur certain costs exercising its right with respect to the
collateral. If a Counterparty becomes bankrupt or otherwise fails to perform its
obligations due to financial difficulties, the Fund may experience significant
delays in obtaining any recovery in a bankruptcy or other reorganization
proceeding. The Fund may obtain only limited recovery or may obtain no recovery
in such circumstances.

Swap agreements may increase or decrease the overall volatility of the
investments of the Fund. The performance of swap agreements may be affected by a
change in the specific interest rate, security, currency, or other factors that
determine the amounts of payments due to and from the Fund. The Fund's maximum
equity price risk to meet its future payments under swap agreements outstanding
at August 31, 2014 is equal to the total notional amount as shown on the
Portfolio of Investments. The notional amount represents the U.S. dollar value
of the contract as of the day of the opening transaction or contract reset.

An interest rate swap agreement involves the Fund's agreement to exchange a
stream of interest payments for another party's stream of cash flows. Interest
rate swaps do not involve the delivery of securities or other underlying assets
or principal. Accordingly, the risk of loss with respect to interest rate swaps
is limited to the net amount of interest payments that the Fund is contractually
obligated to make.

D. SECURITIES TRANSACTIONS:

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.

E. FOREIGN CURRENCY:

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investments and items of income and expense are
translated on the respective dates of such transactions.





NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (CONTINUED)


                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                          AUGUST 31, 2014 (UNAUDITED)


                          3. DERIVATIVES TRANSACTIONS

Written option activity for the Fund for the fiscal year-to-date period
(December 1, 2013 through August 31, 2014) was as follows:

                                                    NUMBER
                                                      OF
WRITTEN OPTIONS                                    CONTRACTS      PREMIUMS
----------------------------------------------------------------------------

Options outstanding at November 30, 2013...           32,393   $  1,571,359
Options Written............................           77,337      4,163,302
Options Expired............................          (37,534)    (1,527,204)
Options Exercised..........................          (22,914)    (1,281,146)
Options Closed.............................          (17,256)    (1,088,069)
                                                  -----------  -------------
Options outstanding at August 31, 2014.....           32,026   $  1,838,242
                                                  ===========  =============

The average volume of interest rate swaps was $40,122,500 for the fiscal
year-to-date period (December 1, 2013 through August 31, 2014).





ITEM 2. CONTROLS AND PROCEDURES.

(a)   The registrant's principal executive and principal financial officers, or
      persons performing similar functions, have concluded that the registrant's
      disclosure controls and procedures (as defined in Rule 30a-3(c) under the
      Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR
      270.30a-3(c))) are effective, as of a date within 90 days of the filing
      date of the report that includes the disclosure required by this
      paragraph, based on their evaluation of these controls and procedures
      required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and
      Rules 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934, as
      amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b)   There were no changes in the registrant's internal control over financial
      reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
      270.30a-3(d)) that occurred during the registrant's last fiscal quarter
      that have materially affected, or are reasonably likely to materially
      affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section 302 of
the Sarbanes-Oxley Act of 2002 are attached hereto.





                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)        First Trust Energy Infrastructure Fund
             -----------------------------------------------------

By (Signature and Title)*               /s/ Mark R. Bradley
                                        ----------------------------------------
                                        Mark R. Bradley
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 24, 2014
     ---------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)*               /s/ Mark R. Bradley
                                        ----------------------------------------
                                        Mark R. Bradley
                                        President and Chief Executive Officer
                                        (principal executive officer)

Date: October 24, 2014
     ---------------------

By (Signature and Title)*               /s/ James M. Dykas
                                        ----------------------------------------
                                        James M. Dykas
                                        Treasurer, Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)

Date: October 24, 2014
     ---------------------

*Print the name and title of each signing officer under his or her signature.