The high thermal conductivity of graphene makes it an important filler material for thermally conductive composite materials. However, the interfacial thermal resistance between the fillers greatly hinders the heat transfer between the fillers. The functionalization of the edges of graphene can introduce covalent or hydrogen bonding between the graphene edge interfaces to replace Van Der Waals (VDWs) interaction connections, which is expected to enhance the interfacial thermal conductance. In this paper, the interfacial heat transfer properties of the graphene chemically functionalized with —COOH groups are systematically studied, and the effects of the distance between graphene sheets and the functionalized density on the interface thermal resistance are discussed. The results show that, as the distance between the edges of the two graphene sheets decreases, the interfacial thermal conduction between the interfaces of the functionalized graphene gradually converges to around 5×108 W/ (m2 ·K), which is an order of magnitude higher than that between the H-terminated graphene. The interfacial thermal conduction shows a non-linear monotonous increase with increasing the functionalization density. Further results show that there is a synergistic effect between the functionalized density and the graphene edge interface spacing. Increasing the functionalized density improves the interaction between the interfaces and reduces the interface spacing between the graphene edges, thereby enhancing the interfacial thermal conduction. The results of this paper provide an important reference for the study of effects of hydrogen bonding on the interfacial heat transfer between graphene fillers.