We study the process e+e-→π+π-ηγ, where the photon is radiated from the initial state. About 8000 fully reconstructed events of this process are selected from the BABAR data sample with an integrated luminosity of 469 fb-1. Using the π+π-η invariant mass spectrum, we measure the e+e-→π+π-η cross section in the e+e- center-of-mass energy range from 1.15 to 3.5 GeV. The cross section is well described by the Vector-Meson dominance model with four ρ-like states. We observe 49±9 events of the J/ψ decay to π+π-η and measure the product ΓJ/Ψ→e+e-BJ/Ψ→π+π-η=2.34±0.43stat±0.16syst eV.