Cubic silicon carbide (3C-SiC) has been grown on Si (111) substrate by chemical vapor deposition. The crystal quality of SiC with the SiCN buffer layer is obviously improved comparing with that grown on the SiC buffer layer. The SiCN film, composed of elemental Si and SiC1-xNx alloy, is formed by the constant-source diffusion of the C and N atoms into the Si substrate. During the 3C-SiC high temperature growth, this in-situ formed SiCN film evolves into a double sub-layered SiCN buffer, including the SiC1-xNx alloy and the SiCN composite sublayers. The SiC1-xNx alloy layer (x from 0 to 0.09) results from the limited-source diffusion of N from the in-situ formed SiCN film to the subsequently deposited SiC. The SiCN composite layer, composed of elemental Si and SiC1-xNx alloy (x from 0.09 to 0.06), is caused by the constant-source diffusion of C from the SiC towards the substrate, as well as the outgoing diffusion of N in the in-situ formed SiCN film. The SiCN buffer layer can effectively accommodate the lattice mismatch between SiC and Si substrate.