We study the three-body charmed baryonic decays B̄0→Σ c++p̄π- and B̄0→Σc0p̄π+ in the four-body final state B̄0→Λc+p̄π+π-, using a data sample of 357fb-1 accumulated at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We measure the branching fractions B(B̄0→Σc(2455)++p̄π-)=(2.1±0.2±0. 3±0.5)×10-4, B(B̄0→Σc(2455)0p̄π+)=(1. 4±0.2±0.2±0.4)×10-4 and B(B̄0→Σ c(2520)++p̄π-)=(1.2±0.1±0.2±0.3)×10-4 with signal significances of 13.1σ, 9.4σ and 7.1σ, respectively. The errors are statistical, systematic, and due to the uncertainty in B(Λc+→pK-π+), respectively. We also set an upper limit B(B̄0→Σc(2520)0p̄π+)<0.38×10-4 at the 90% confidence level. In addition, we obtain a nonresonant branching fraction of (6.4±0.4±0.9±1.7)×10-4, and a total branching fraction of (11.2±0.5±1.4±2.9)×10-4 for B̄0→Λc+p̄π+π-. © 2007 The American Physical Society.