As an analogue to an electrical diode, a radiative thermal diode allows radiation to transfer more efficiently in one direction than in the opposite direction by operating in a contactless mode. In this study, we demonstrated that within the framework of three-body photon thermal tunneling, the rectification performance of a three-body radiative diode can be greatly improved by bringing graphene into the system. The system is composed of three parallel slabs, with the hot and cold terminals of the diode coated with graphene films and the intermediate body made of vanadium dioxide (VO2). The rectification factor of the proposed radiative thermal diode reaches 300% with a 350 nm separation distance between the hot and cold terminals of the diode. With the help of graphene, the rectification performance of the radiative thermal diode can be improved by over 11 times. By analyzing the spectral heat flux and energy transmission coefficients, it was found that the improved performance is primarily attributed to the surface plasmon polaritons (SPPs) of graphene. They excite the modes of insulating VO2 in the forward-biased scenario by forming strongly coupled modes between graphene and VO2 and thus dramatically enhance the heat flux. However, for the reverse-biased scenario, the VO2 is at its metallic state, and thus, graphene SPPs cannot work by three-body photon thermal tunneling. Furthermore, the improvement was also investigated for different chemical potentials of graphene and geometric parameters of the three-body system. Our findings demonstrate the feasibility of using thermal-photon-based logical circuits, creating radiation-based communication technology and implementing thermal management approaches at the nanoscale.