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We report a study of the e+e– → D+D–π+π– process using e+e– collision data samples with an integrated luminosity of 2.5 fb–1 at center-of-mass energies from 4.36 to 4.60GeV, collected with the BESIII detector at the BEPCII storage ring. The D1(2420)+ is observed in the D+π+π– mass spectrum. The mass and width of the D1(2420)+ are measured to be (2427.2 ± 1.0stat. ± 1.2syst.)MeV/c2 and (23.2 ± 2.3stat. ± 2.3syst.)MeV, respectively. The first errors are statistical and the second ones are systematic. In addition, the Born cross sections of the e+e– → D1(2420)+ D– + c.c. → D+D–π+π– and e+e– → ψ(3770)π+π– → D+D–π+π– processes are measured as a function of the center-of-mass energy.