Polycarbosilane was synthesized by the Kumada rearrangement of polydimethylsilane in the presence of zeolite (ZSM-5) as a catalyst at $350^{circ}C$. The prepared polycarbosilane had very low molecular weight ($M_w=500$), so that it was not suitable to fabricate SiC fiber by melt spinning. Further polymerization of PCS was conducted around $400^{circ}C$ to obtain spinnable polycarbosilane. After polymerization, the polycarbosilanes were isolated by distillation according to the molecular weight distributions. The PCS with a controlled molecular weight distribution was spun into continuous polycarbosilane green fibers. The PCS green fiber was successfully transformed into silicon oxycarbide fiber. The room temperature strength of the SiC fiber was around 1.5 - 1.8 GPa. The oxidation behavior and the tensile strength after oxidation were also evaluated.