EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER

      Pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the
Sarbanes-Oxley Act of 2002, the undersigned officer of Leap Wireless
International, Inc. (the "Company") hereby certifies, to such officer's
knowledge, that:

      (a) the accompanying Quarterly Report on Form 10-Q of the Company for the
quarterly period ended June 30, 2004 (the "Report") fully complies with the
requirements of Section 13(a) or Section 15(d), as applicable, of the Securities
Exchange Act of 1934, as amended; and

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

Dated: August 11, 2004                               /s/ William M. Freeman
                                                     ---------------------------
                                                     William M. Freeman
                                                     Chief Executive Officer

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