The cross section for the process e+e-→π+π-J/ψ is measured precisely at center-of-mass energies from 3.77 to 4.60 GeV using 9 fb-1 of data collected with the BESIII detector operating at the BEPCII storage ring. Two resonant structures are observed in a fit to the cross section. The first resonance has a mass of (4222.0±3.1±1.4) MeV/c2 and a width of (44.1±4.3±2.0) MeV, while the second one has a mass of (4320.0±10.4±7.0) MeV/c2 and a width of (101.4-19.7+25.3±10.2) MeV, where the first errors are statistical and second ones are systematic. The first resonance agrees with the Y(4260) resonance reported by previous experiments. The precision of its resonant parameters is improved significantly. The second resonance is observed in e+e-→π+π-J/ψ for the first time. The statistical significance of this resonance is estimated to be larger than 7.6σ. The mass and width of the second resonance agree with the Y(4360) resonance reported by the BABAR and Belle experiments within errors. Finally, the Y(4008) resonance previously observed by the Belle experiment is not confirmed in the description of the BESIII data.