We present a measurement of the CP-violating asymmetry in B0→ρ+ρ- decays using 535×106 BB̄ pairs collected with the Belle detector at the KEKB e+e- collider. We measure CP-violating coefficients A=0.16±0.21(stat)±0.08(syst) and S=0.19±0. 30(stat)±0.08(syst). These values are used to determine the unitarity triangle angle 2 using an isospin analysis; the solution consistent with the standard model lies in the range 54°< 2<113° at the 90% confidence level. © 2007 The American Physical Society.