  We study the process $e^+e^-\to J/\psi\pi^{+}\pi^{-}$ 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 10.58 and 10.54 GeV, and correspond to an integrated luminosity of 454
$\mathrm{fb^{-1}}$. We investigate the $J/\psi \pi^{+}\pi^{-}$ mass
distribution in the region from 3.5 to 5.5 $\mathrm{GeV/c^{2}}$. Below 3.7
$\mathrm{GeV/c^{2}}$ the $\psi(2S)$ signal dominates, and above 4
$\mathrm{GeV/c^{2}}$ there is a significant peak due to the Y(4260). A fit to
the data in the range 3.74 -- 5.50 $\mathrm{GeV/c^{2}}$ yields a mass value
$4244 \pm 5$ (stat) $ \pm 4$ (syst)$\mathrm{MeV/c^{2}}$ and a width value $114
^{+16}_{-15}$ (stat)$ \pm 7$(syst)$\mathrm{MeV}$ for this state. We do not
confirm the report from the Belle collaboration of a broad structure at 4.01
$\mathrm{GeV/c^{2}}$. In addition, we investigate the $\pi^{+}\pi^{-}$ system
which results from Y(4260) decay.
