Cubic-SiC was grown on Si substrates by a combination of carbonization and consecutive chemical vapor deposition. Grown layer on the (100) and (111) substrates were single crystalline cubic-SiC. Those on the (110) and (211) were poly-crystalline. This difference was due to the difference in crystallinity of carbonized buffer layers. In order to explain the origin of such a result the initial stage of carbonization and atomic arrangements around the interface between Si and SiC were discussed. Grown layers on Si (100) show good crystallinity and the flattest surface among grown layers on these 4 kinds of substrates. However, texture-like morphology was observed, which originated from antiphase domains (APD). Off orientation towards (011) was found to be effective to eliminate APD, which was clarified by the growth on a spherically polished Si (100) substrate. The origin and elimination mechanism of APD were also discussed.