Based on the relationship between traditional gas stations and electric vehicle charging stations in the automotive fuel market, the static Cournot model with profit maximization as the objective function and a dynamic one based on difference method are established to get the Cournot equilibrium of every fuel station. Numerical simulation and sensitivity analysis show feasibility and robustness of the model. All results acquired can be used in the electric vehicle charging stations and the traditional gas stations in the automobile fuel market for output policy guidance.