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

I, James A. Bowen, Chairman of the Board, 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: December 22, 2011         /s/ James A. Bowen
                                ------------------------------------------------
                                James A. Bowen, Chairman of the Board, President
                                and Chief Executive Officer
                                (principal executive officer)



I, Mark R. Bradley, 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: December 22, 2011         /s/ Mark R. Bradley
                                ------------------------------------------------
                                Mark R. Bradley, Treasurer, Chief
                                Financial Officer and Chief Accounting Officer
                                (principal financial officer)