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

                                  FORM N-CSR/A

        CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT
                                   COMPANIES

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

                     First Trust Energy Infrastructure Fund
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               (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: May 31, 2015
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Form N-CSR is to be used by management investment companies to file reports with
the Commission not later than 10 days after the transmission to stockholders of
any report that is required to be transmitted to stockholders under Rule 30e-1
under the Investment Company Act of 1940 (17 CFR 270.30e-1). The Commission may
use the information provided on Form N-CSR in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-CSR,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-CSR
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 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.





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                                EXPLANATORY NOTE

      This amendment to the Form N-CSR of the First Trust Energy Infrastructure
Fund (the "Fund") is being filed to correct the reference to the Period of
Report on the Fund's submission filing. The Period of Report from the original
filing of such Form N-CSR (the "Original Filing") made on August 3, 2015 was
inadvertently referred to as May 31, 2014. Except as otherwise noted above, the
Original Filing was accurate, timely distributed to shareholders and contained
all other information required to be included in such reports by the Company's
registration statement form under the Investment Company Act of 1940, as
amended, pursuant to Rule 30e-1(a) thereunder.

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

Date: December 1, 2015
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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: December 1, 2015
     ------------------

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

Date: December 1, 2015
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* Print the name and title of each signing officer under his or her signature.