Exhibit 99.1

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 CellStar Corporation (the “Registrant”) on Form 10-Q for the quarterly period ended May 31, 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: July 15, 2003

A signed original of this written statement required by Section 906 has been provided to CellStar Corporation and will be retained by CellStar Corporation and furnished to the Securities and Exchange Commission or its staff upon request.