We report on novel superconducting characteristics of the heavy fermion (HF) superconductor CePt3Si without inversion symmetry through 195 Pt-NMR study on a single crystal with Tc = 0.46 K that is lower than Tc ∼ 0.75 K for polycrystals. We show that the intrinsic superconducting characteristics inherent to CePt3Si can be understood in terms of the unconventional strong-coupling state with a line-node gap below Tc = 0.46 K. The mystery about the sample dependence of Tc is explained by the fact that more or less polycrystals and single crystals inevitably contain some disordered domains, which exhibit a conventional BCS s-wave superconductivity (SC) below 0.8 K. In contrast, the Néel temperature TN ∼ 2.2 K is present regardless of the quality of samples, revealing that the Fermi surface responsible for SC differ from that for the antiferromagnetic order. These unusual characteristics of CePt3Si can be also described by a multiband model; in the homogeneous domains, the coherent HF bands are responsible for the unconventional SC, whereas in the disordered domains the conduction bands existing commonly in LaPt3Si may be responsible for the conventional s-wave SC. We remark that some impurity scatterings in the disordered domains break up the 4f-electrons-derived coherent bands but not others. In this context, the small peak in 1/T1 just below Tc reported in the previous paper (Yogi et al, (2004)) is not due to a two-component order parameter composed of spin-singlet and spin-triplet Cooper pairing states, but due to the contamination of the disorder domains which are in the s-wave SC state.as compared to a Pauli limiting field. 15-17) This kind of behavior has never been observed in the other HF superconductors such as CeCoIn 5 , CeIrIn 5 , and CeCu 2 Si 2 , which are in a spin-singlet Cooper pairing regime. In the noncentrosymmetric superconductors where the correlation between electrons may be not so significant, however, the characteristic feature for conventional s-wave spin singlet superconducting state has been observed in many compounds, for example, Y 2 C 3 , 18, 19) Ir 2 Ga 9 , 20, 21) LaPt 3 Si, 22) LaIrSi 3 , 23) Li 2 Pd 3 B, 24) and so on, whereas the parity mixing state has been argued only in the related compound Li 2 Pt 3 B. 25,26) The CePt 3 Si exhibits superconductivity at T c = 0.75 K in an antiferromagnetically ordered state below a Néel temperature of T N = 2.2 K, as reported by Bauer et al. 9,27) Neutron-scattering measurement probed an AFM structure with a wave vector Q = (0, 0, 1/2) and a magnetic moment of 0.16µ B lying in the ab-plane of the tetragonal lattice. 28) Uniform coexistence of the AFM order and SC has been microscopically evidenced by NMR 29, 30) and µSR. 31) Although CePt 3 Si has attracted considerable attention as the first superconductor without inversion symmetry, 3-8) the experimental results are still contradictory. For example, the London penetration depth, 32) thermal conductivity, 33) and NMR 29) revealed J. Phys. Soc. Jpn.