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 Annual Report of CellStar Corporation (the “Registrant”) on Form 10-K for the fiscal year ended November 30, 2003, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned hereby certifies, in the capacity as indicated below and pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

1. 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.

/s/ Terry S. Parker                                    

Terry S. Parker, Chief Executive Officer

Date: February 25, 2004