In the production of SiC electronic devices, one of the main challenges is the fabrication of good Ohmic contacts due to the difficulty in finding the metals with low Schottky barriers of wide band gap SiC. Therefore, reducing the Schottky barrier height (SBH) at the metal/SiC interface is of great importance. In this paper, the effects of graphene intercalation on the SBH in different metals (Ag, Ti, Cu, Pd, Ni, Pt)/4H-SiC interfaces are studied by combining the average electrostatic potential and local density of states calculation methods based on first-principles plane wave pseudopotential density functional theory. The calculation results show that single-layer graphene intercalation can reduce the SBH of metal/4H-SiC contact. When the two layers of graphene are inserted, the SBH are further reduced. Especially, the contact between Ni and Ti exhibits negative SBH values, inferring that good Ohmic contacts are formed. When layers of graphene continue to increase, the SBH no longer changes obviously. By analyzing the differential charge density and the local density of states of the interface, the mechanism of SBH reduction may be that the dangling bonds on the SiC surface are saturated by the graphene C atoms and the influence of the metal-induced energy gap state at the interface is reduced, thereby reducing the interface state density. In addition, graphene and the corresponding new phases at the interface have low work functions. Moreover, an interfacial electric dipole layer may be formed at the SiC/graphene interface which also contributes to barrier reduction.