EXHIBIT 32.1

                        CERTIFICATION PURSUANT TO
                         18 U.S.C. SECTION 1350,
                   AS ADOPTED PURSUANT TO SECTION 906
                   OF THE SARBANES-OXLEY ACT OF 2002


     In connection with the Quarterly Report of Giant Industries, Inc.
("Giant") on Form 10-Q for the quarter ending June 30, 2004, as filed
with the Securities and Exchange Commission on the date hereof (the
"Report"), I, Fred L. Holliger, Chief Executive Officer of Giant,
certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to
Section 906 of the Sarbanes-Oxley Act of 2002, that:

     (a) The Report fully complies with the requirements of Section 13(a)
or 15(d) of the Securities Exchange Act of 1934; and

     (b) The information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of
Giant.


                             By: /s/ FRED L. HOLLIGER
                                --------------------------------
                             Name:   Fred L. Holliger
                             Title:  Chief Executive Officer

Date: August 11, 2004.