CERTIFICATION PURSUANT TO RULE 30A-2(B) UNDER THE 1940 ACT AND SECTION 906
                           OF THE SARBANES-OXLEY ACT

I, Mark R. Bradley, President and Chief Executive Officer of First Trust
Mortgage Income Fund (the "Registrant"), certify that:

      1.    The Form N-CSR of the Registrant (the "Report") fully complies with
            the requirements of Section 13(a) or 15(d) of the Securities
            Exchange Act of 1934, as amended; and

      2.    The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: Decemnber 23, 2014                /s/ Mark R. Bradley
     ----------------------------       ----------------------------------------
                                        Mark R. Bradley, President
                                        and Chief Executive Officer
                                        (principal executive officer)





I, James M. Dykas, Treasurer, Chief Financial Officer and Chief Accounting
Officer of First Trust Mortgage Income Fund (the "Registrant"), certify that:

      1.    The Form N-CSR of the Registrant (the "Report") fully complies with
            the requirements of Section 13(a) or 15(d) of the Securities
            Exchange Act of 1934, as amended; and

      2.    The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: Decemnber 23, 2014                /s/ James M. Dykas
     ----------------------------       ----------------------------------------
                                        James M. Dykas, Treasurer, Chief
                                        Financial Officer and Chief Accounting
                                        Officer (principal financial officer)