Both suspended graphene and graphene on Si-terminated (0001) SiC system with the lattice parameter of 4.92 angstrom (strained) or 5.33 angstrom (unstrained) were simulated using first-principles method to investigate the substrate effect on thermal transport properties of graphene on SiC. The thermal conductance of graphene on substrate is figured out to have a dramatical reduction, with a maximum value of 42% which can only be found on the buffer graphene layer, compared to that of suspended graphene at room temperature. The results will help to accelerate application of graphene in the situation where substrate effect cannot be ignored. (C) 2014 Elsevier B.V. All rights reserved.