Using a data sample of 772 x 10(6) B (B) over bar pairs collected on the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider, we report the observation of B-0 -> p (p) over bar pi(+)pi(-) and the first observation of B+ -> p (p) over bar pi(+)pi(0). We measure a decay branching fraction of (0.83 +/- 0.17 +/- 0.17) x 10(-6) in B-0 -> p (p) over bar pi(+)pi(-) for M pi+pi- < 1.22 GeV/c(2) with a significance of 5.5 standard deviations. The contribution from B-0 -> p (p) over barK(0) is excluded. We measure a decay branching fraction of (4.58 +/- 1.17 +/- 0.67) x 10(-6) for B+ -> p (p) over bar pi(+)pi(0 )with M pi+pi 0 < 1.3 GeV/c(2) with a significance of 5.4 standard deviations. We study the difference of the M-p((p) over bar) distributions in B-0 -> p (p) over bar pi(+)pi(-) and B-0 -> p (p) over bar pi(+)pi(0).