Exhibit 31.1

CERTIFICATION OF CEO PURSUANT TO

RULE 13A-14(A) OF THE SECURITIES EXCHANGE ACT OF 1934

I, John J. Legere,
Chief Executive Officer of Global Crossing Limited, certify that:

1. I have reviewed this quarterly report on
Form 10-Q of Global Crossing Limited;

2. Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial information included in this report, fairly
present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this report;

4. The registrants other certifying officer and I are responsible for establishing and maintaining disclosure
controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a15(f) and 15d15(f)) for the registrant and have:

(a) Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to
be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is
being prepared;

(b) Designed such internal control over financial reporting, or caused such
internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with
generally accepted accounting principles;

(c) Evaluated the effectiveness of the
registrants disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

(d) Disclosed in this report any change in the registrants internal control over
financial reporting that occurred during the registrants most recent fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrants internal control over financial reporting; and

5. The registrants other certifying officer and I have disclosed, based on our most recent evaluation of internal
control over financial reporting, to the registrants auditors and the audit committee of the registrants board of directors (or persons performing the equivalent functions):

(a) All significant deficiencies and material weaknesses in the design or operation of internal control
over financial reporting which are reasonably likely to adversely affect the registrants ability to record, process, summarize and report financial information; and

(b) Any fraud, whether or not material, that involves management or other employees who have a significant
role in the registrants internal control over financial reporting.



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|Date: November 3, 2010 
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|/S/ JOHN J. LEGERE     
|John J. Legere         
|Chief Executive Officer