The cross section for e(+)e(-)-->pi(+)pi(-)J/psi between 3.8 and 5.5 GeV/c(2) is measured using a 548 fb(-1) data sample collected on or near the Upsilon(4S) resonance with the Belle detector at KEKB. A peak near 4.25 GeV/c(2), corresponding to the so called Y(4260), is observed. In addition, there is another cluster of events at around 4.05 GeV/c(2). A fit using two interfering Breit-Wigner shapes describes the data better than one that uses only the Y(4260), especially for the lower-mass side of the 4.25 GeV enhancement.