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Satellite networks, as a supplement to terrestrial networks, can provide effective computing services for Internet of Things (IoT) users in remote areas. Due to the resource limitation of satellites, such as in computing, storage, and energy, a computation task from a IoT user can be divided into several parts and cooperatively accomplished by multiple satellites to improve the overall operational efficiency of satellite networks. Network function virtualization (NFV) is viewed as a new paradigm in allocating network resources on-demand. Satellite edge computing combined with the NFV technology is becoming an emerging topic. In this paper, we propose a potential game approach for virtual network function (VNF) placement in satellite edge computing. The VNF placement problem aims to maximize the number of allocated IoT users, while minimizing the overall deployment cost. We formulate the VNF placement problem with maximum network payoff as a potential game and analyze the problem by a game-theoretical approach. We implement a decentralized resource allocation algorithm based on a potential game (PGRA) to tackle the VNF placement problem by finding a Nash equilibrium. Finally, we conduct the experiments to evaluate the performance of the proposed PGRA algorithm. The simulation results show that the proposed PGRA algorithm can effectively address the VNF placement problem in satellite edge computing.