This study characterizes the structure effect on interfacial thermal resistance of nanofilm. Through the nonequilibrium molecular dynamics (NEMD) method and the equilibrium molecular dynamics (EMD) method, this simulation compares the interfacial thermal resistances between graphene and crystalline silicon with symmetric and asymmetric structure, and proves the structure effect of graphene. It reveals that the interfacial thermal resistance of symmetric structure is greater than asymmetric structure. At 300K, for a single layer graphene, the interfacial thermal resistance of symmetric structure is at least 30% more than asymmetric structure. The interfacial thermal resistances increase with the thickness increase of the graphene, while the relative variations between the interfacial thermal resistances of symmetric and asymmetric structure decrease. When the layer numbers of graphene more than 4, the interfacial thermal resistance tends to be constant and the structure effect can be neglected.