Due to the graphene’s exceptional thermal conductivity, it is widely used to increase overall thermal properties of polymer nanocomposites. The interfacial thermal properties between the graphene and the polymer matrix is important for determining the thermal performance of nanocomposites. In this study, heat transport behaviors within graphene/epoxy nanocomposites are studied using molecular dynamics (MD) simulations. A model of cross-linked epoxy system consisting of EPON 862 (diglycidyl ether of bisphenol F, DGEBF) resin and diethyltoluenediamine (DETDA) curing agent is established. The effect of the degree of cross-linking on the molecular motion of the epoxy system is also emphasized. Furthermore, the interfacial thermal resistance and thermal conductivity of graphene/epoxy nanocomposites are systematically investigated. Our findings provide a better understanding of the heat transport behaviors within polymer nanocomposites and should be useful for future development of various thermal management applications.