Exhibit 31

Rule 13a-14(d)/15d-14(d) Certification

I, Paul Vanderslice, certify that:



|1. | I have reviewed this report on Form 10-K, and all reports on Form 10-D required to be filed in respect of the period covered by this report on Form 10-K, of Citigroup Commercial Mortgage Trust 2013-GCJ11 (the
Exchange Act Periodic Reports);
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|2. | Based on my knowledge, the Exchange Act Periodic Reports, taken as a whole, do 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;
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|3. | Based on my knowledge, all of the distribution, servicing and other information required to be provided under Form 10-D for the period covered by this report is included in the Exchange Act Periodic Reports;
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|4. | Based on my knowledge and the servicer compliance statement(s) required in this report under Item 1123 of Regulation AB, and except as disclosed in the Exchange Act Periodic Reports, the servicers have fulfilled
their obligations under the servicing agreement(s) in all material respects; and
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|5. | All of the reports on assessment of compliance with servicing criteria for asset-backed securities and their related attestation reports on assessment of compliance with servicing criteria for asset-backed securities
required to be included in this report in accordance with Item 1122 of Regulation AB and Exchange Act Rules 13a-18 and 15d-18 have been included as an exhibit to this report, except as otherwise disclosed in this report. Any material instances
of noncompliance described in such reports have been disclosed in this report on Form 10-K.
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In giving the certifications above, I have
reasonably relied on information provided to me by the following unaffiliated parties: Wells Fargo Bank, National Association, as master servicer; LNR Partners, LLC, as special servicer; U.S. Bank National Association, as custodian; Pentalpha
Surveillance LLC, as operating advisor; CoreLogic Commercial Real Estate Services, Inc., as servicing function participant; National Tax Search, LLC, as servicing function participant; Newmark Realty Capital, Inc., as servicing function participant;
Wells Fargo Bank, National Association, as master servicer for the Empire Hotel & Retail Mortgage Loan and the National Harbor Mortgage Loan; LNR Partners, LLC as special servicer for the Empire Hotel & Retail Mortgage Loan and the
National Harbor Mortgage Loan; CoreLogic Commercial Real Estate Services, Inc., as servicing function participant for the Empire Hotel & Retail Mortgage Loan and the National Harbor Mortgage Loan; National Tax Search, LLC, as servicing
function participant for the Empire Hotel & Retail Mortgage Loan and the National Harbor Mortgage Loan; Wells Fargo Bank, National Association, as certificate administrator and custodian for the Empire Hotel & Retail Mortgage Loan
and the National Harbor Mortgage Loan; and Trimont Real Estate Advisors, Inc., as operating advisor for the Empire Hotel & Retail Mortgage Loan and the National Harbor Mortgage Loan.

Date: March 30, 2016

/s/ Paul
Vanderslice

Paul Vanderslice

President, Citigroup Commercial Mortgage

Securities Inc.

(senior officer in charge of securitization of the depositor)