This paper investigates the variation of hole concentration with temperature, then discussed the effect of hole concentration , base and temperature on the density of metal - based epitaxial graphene. The results were three fold. First, the hole concentration increases nonlinearly with the temperature increasing, and the rate of change of the hole concentration of the epitaxial graphene with the temperature is smaller than that of graphene. Second, Compared with graphene,When electron energy is zero, the density of states of copper-based epitaxial graphene is higher than that of graphene. Third, the maximum of graphene density decreases at the corresponding electron energy because of the substrate. The density of states of Cu-based epitaxial graphene decreases with the increase of hole concentration and temperature, with the change of the concentration of the hole is linear, but with the temperature change is nonlinear.