The cross section for e+e -→π+π-J/ψ between 3.8 and 5.5 GeV is measured with a 967 fb-1 data sample collected by the Belle detector at or near the Υ(nS) (n=1,2,...,5) resonances. The Y(4260) state is observed, and its resonance parameters are determined. In addition, an excess of π+π-J/ψ production around 4 GeV is observed. This feature can be described by a Breit-Wigner parametrization with properties that are consistent with the Y(4008) state that was previously reported by Belle. In a study of Y(4260)→π+π-J/ψ decays, a structure is observed in the M(π±J/ψ) mass spectrum with 5.2σ significance, with mass M=(3894.5±6.6±4. 5) MeV/c2 and width Γ=(63±24±26) MeV/c2, where the errors are statistical and systematic, respectively. This structure can be interpreted as a new charged charmoniumlike state.