We study the process e + e − → J / ψ π + π − 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 10.58 and 10.54 GeV, and correspond to an integrated luminosity of 454     fb − 1 . We investigate the J / ψ π + π − mass distribution in the region from 3.5 to 5.5     GeV / c 2 . Below 3.7     GeV / c 2 the ψ ( 2 S ) signal dominates, and above 4     GeV / c 2 there is a significant peak due to the Y ( 4260 ) . A fit to the data in the range 3.74 - 5.50     GeV / c 2 yields a mass value 4245 ± 5 ( stat ) ± 4 ( syst )     MeV / c 2 and a width value 114 + 16 − 15 ( stat ) ± 7 ( syst )     MeV for this state. We do not confirm the report from the Belle Collaboration of a broad structure at 4.01     GeV / c 2 . In addition, we investigate the π + π − system which results from Y ( 4260 ) decay.