We study charmless B+ meson decays to the p Lambda pi(+)pi(-) final state using a 605 fb(-1) data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. There are significant signals found with the p Lambda mass peaking near threshold. The observed branching fraction for nonresonant B+-> p Lambda pi(+)pi(-) is (5.92(-0.84)(+0.88)(stat)+/- 0.69(syst))x10(-6) with a significance of 9.1 standard deviations. We also observe the intermediate three-body decay B+-> p Lambda rho(0) with a branching fraction of (4.78(-0.64)(+0.67)(stat)+/- 0.60(syst))x10(-6) and a significance of 9.5 standard deviations, and find a hint of a B+-> p Lambda f(2)(1270) signal. No other intermediate three-body decay is found in this study.