Exhibit 31.1

I, Chris A. Choate, certify that:



| | 1. | I have reviewed this report on Form 10-K/A and all reports on Form 10-D required to be filed in respect of the period covered by this report on Form 10-K/A of AmeriCredit Automobile Receivables Trust 2013-1 (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 required in this report under Item 1123 of Regulation AB, and except as disclosed in the Exchange Act periodic reports, the servicer has fulfilled its
obligations under the servicing agreements 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/A.
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In giving the certifications above, I have
reasonably relied on information provided to me by the following unaffiliated parties: The Bank of New York Mellon.

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|       |  |                                                     
|By:    |  | /s/ Chris A. Choate                                  |  | 
|Name:  |  | Chris A. Choate                                      |  | 
|Title: |  | Executive Vice President and Chief Financial Officer |  | 
|Date:  |  | June 16, 2015                                        |  |