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

I, George R. Aylward, President of The Zweig Fund, Inc. (the "Registrant"),
certify that:

    1. The Form N-CSR of the Registrant containing the financial statements
       (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: September 9, 2011      /s/ George R. Aylward
                             ------------------------------
                             George R. Aylward, President
                             (principal executive officer)

I, W. Patrick Bradley, Treasurer of The Zweig Fund, Inc. (the "Registrant"),
certify that:

    1. The Form N-CSR of the Registrant containing the financial statements
       (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: September 9, 2011      /s/ W. Patrick Bradley
                             ------------------------------
                             W. Patrick Bradley, Treasurer
                             (principal financial officer)