Global Crossing (GBLXQ) 10-Q 2005 Q2 Quarterly report

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 Global Crossing Limited (the “registrant”) on Form 10-Q for the period ending June 30, 2005 as filed with the Securities and Exchange Commission on the date hereof (the “report”), I, John J. Legere, Chief Executive Officer of the registrant, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) The report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; 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: August 9, 2005

/s/    JOHN J. LEGERE        

John J. Legere

Chief Executive Officer