© 2015 American Physical Society. We report measurement of the cross section of e+e-→π+π-ψ(2S) between 4.0 and 5.5 GeV, based on an analysis of initial state radiation events in a 980fb-1 data sample recorded with the Belle detector. The properties of the Y(4360) and Y(4660) states are determined. Fitting the mass spectrum of π+π-ψ(2S) with two coherent Breit-Wigner functions, we find two solutions with identical mass and width but different couplings to electron-positron pairs: MY(4360)=(4347±6±3)MeV/c2, ΓY(4360)=(103±9±5)MeV, MY(4660)=(4652±10±8)MeV/c2, ΓY(4660)=(68±11±1)MeV; and B[Y(4360)→π+π-ψ(2S)]·ΓY(4360)e+e-=(10.9±0.6±0.7)eV and B[Y(4660)→π+π-ψ(2S)]·ΓY(4660)e+e-=(8.1±1.1±0.5)eV for one solution; or B[Y(4360)→π+π-ψ(2S)]·ΓY(4360)e+e-=(9.2±0.6±0.6)eV and B[Y(4660)→π+π-ψ(2S)]·ΓY(4660)e+e-=(2.0±0.3±0.2)eV for the other. Here, the first errors are statistical and the second systematic. Evidence for a charged charmoniumlike structure at 4.05GeV/c2 is observed in the π±ψ(2S) intermediate state in the Y(4360) decays.