Superconductivity and magnetism in the non-centrosymmetric heavy fermion compound CePt3Si and related materials are theoretically investigated. Oil the basis of the random phase approximation (RPA) analysis of the extended Hubbard model, we describe the helical spin fluctuation induced by the Rashba-type anti-symmetric spin-orbit coupling and identify two stable superconducting phases with either the dominant p-wave (s+P-wave) symmetry or file d-wave (p+D+f-wave) symmetry. The effect of the coexistent antiferromagnetic order is investigated in both states. The superconducting order parameter, quasiparticle density of state, NMR 1/T1T, specific heat, anisotropy of H-c2, and possible multiple phase transitions are discussed in detail. A comparison with experimental results indicates that the s+P-wave superconducting state is likely realized in CePt3Si.