In this work, multilayer graphene (MLG), graphene oxide (GO) and carbon nanotube (CNT) are studied as fillers in epoxy resin to enhance thermal transport properties of polymer thermal interface material (TIM). The MLG/CNT filler significantly enhances the thermal conductivity of the epoxy matrix material, increasing thermal conductivity by about 553% at 25 wt% load. At the same time, theoretical models are used to predict the thermal conductivity of TIM, and the model predictions are in a reasonable agreement with the experimental values. We also analyzed the thermal contact resistance (TCR) at the interface between the experimentally obtained TIM and solid in detail. The TCR measured at a pressure of 0.75 MPa is 42.8 mm2·K/W, which was reduced by a factor of 86.7 % compared to the absence of TIMs (The TCR without adding any thermal interface material is 321.8mm2·K/W). It is also established that although MLG contributes more to the thermal conductivity of epoxy resin than GO, GO/epoxy composites are superior to MLG/epoxy composites in reducing the total TCR of solid-solid interface. Our results provide a guideline to enhance thermal transport properties of epoxy resin-based carbon nanocomposites as thermal interface materials (TIMs) for various thermal management applications.