Partial discharge (PD) sensors have been widely used in PD detection of power equipment. In order to adapt to the development of the new power system, the new PD sensor should not only have a wide response band but also have a large dynamic range. PD measurement devices currently used in smart grids are mainly based on traditional metal materials, which face difficulty in fully meeting these technical requirements. Graphene has a variety of excellent properties, and it is introduced to improve PD sensor materials in this paper. Based on the transmission line model, the circuit parameters of graphene PD sensor electrode plate material are theoretically derived. Various factors affecting its resistance characteristics, inductance characteristics, and capacitance characteristics are analyzed. Next, the variation curves of circuit parameters under different influencing factors are obtained. Linear regression models based on the least-square method were developed for circuit parameters. Finally, the simulation and experiment verified that the graphene PD sensor has high gain characteristics. The simulation results are consistent with the experimental results, further verifying the feasibility of the circuit parameter study. This study can be used to guide the design of the new graphene PD sensors.