A distributed mission planning method based on potential game is proposed for the multi-spacecraft system in this paper. First, a mission planning model is established for multi-spacecraft system, by taking into account various constraints, such as spacecraft functionality, fuel capacity, mission deadlines, and the required number of spacecraft for the mission. Second, the mission planning model is mapped to the game model. Then, a simplified algorithm is proposed to obtain the feasible strategy set for spacecraft. Additionally, a distributed mission planning algorithm based on potential game is proposed for multi-spacecraft, which enables the system to obtain a mission planning scheme that maximizes the global return. Finally, the proposed algorithm is verified by using the mission environment of the multi-spacecraft system, which demonstrates the feasibility and effectiveness of the method.