We study the process e(+)e(-) -> psi(2S)pi(+)pi(-) with initial-state-radiation events produced at the PEP-II asymmetric-energy collider. The data were recorded with the BABAR detector at center-of-mass energies at and near the (nS) (n = 2, 3, 4) resonances and correspond to an integrated luminosity of 520 fb(-1). We investigate the psi(2S)pi(+)pi(-) mass distribution from 3.95 to 5.95 GeV/c(2), and measure the center-of-mass energy dependence of the associated e(+)e(-) -> psi(2S)pi(+)pi(-) cross section. The mass distribution exhibits evidence of two resonant structures. A fit to the psi(2S)pi(+)pi(-) mass distribution corresponding to the decay mode psi(2S) -> J/psi pi(+)pi(-) yields a mass value of 4340 +/- 16 (stat) +/- 9 (syst) MeV/c(2) and a width of 94 +/- 32 (stat) +/- 13 (syst) MeV for the first resonance, and for the second a mass value of 4669 +/- 21 (stat) +/- 3 (syst) MeV/c(2) and a width of 104 +/- 48 (stat) +/- 10 (syst) MeV. In addition, we show the pi(+)pi(-) mass distributions for these resonant regions.