Epitaxial growth processes for SiC polytypes in which a SiC substrate is employed are studied using a layered growth model. The corresponding phase diagrams of epitaxial growth processes are given. First-principles calculations are used to determine the parameters in the layered growth model. The layered growth phase diagrams show that when the rearrangement of atoms in one surface Si-C bilayer is allowed, the 3C-SiC structure is formed. When the rearrangement of atoms in two surface Si-C bilayers is allowed, the 4H-SiC structure is formed. When the rearrangement of atoms in more than two surface Si-C bilayers, excepting the case of five surface Si-C bilayers, is allowed, the 6H-SiC structure is formed, which is also shown to be the ground state structure. When the rearrangement of atoms in five surface Si-C bilayers is allowed, the 15R-SiC structure is formed. Thus the 3C-SiC phase would grow epitaxially at low temperature, the 4H-SiC phase would grow epitaxially at intermediate temperature and the 6H-SiC or 15R-SiC phases would grow epitaxially at higher temperature.