Using the constrained-path Monte Carlo method, a two-orbital model for the pnictide superconductors is studied at half filling and in both the electron-and hole-doped cases. At half filling, a stable (π, 0)/(0, π) magnetic order is explicitly observed, and the system tends to be in an orthomagnetic order rather than the striped antiferromagnetic order when increasing the Coulomb repulsion U . In the electron-doped case, the (π, 0)/(0, π) magnetic order is enhanced upon doping and suppressed eventually, and a s± pairing state dominates all the possible nearest-neighbor-bond pairings. Whereas in the hole-doped case, the magnetic order is straightforwardly suppressed and two nearly degenerate A1g and B1g intraband pairings become the dominant ones.