The bilateral trading platform is an intermediary system which serves both consumers and suppliers. To make this happen, platforms must attract users on board from both sides and make them trade with each other. Spatial distribution of suppliers has the significant impact on consumers platform adoption decision, but how does the supplier’s network affect the platform competition has rarely been studied. In this paper, the supplier’s spatial network is added to bilateral trading platform network effect model, and influences of the supplier’s network structure on the platform competition are discussed. Simulation results show that, compared with the central network, the decentralized network is more conducive to the platform competition. When suppliers on two competitive platforms follow the same network structure, the reinforcement effect of the first-mover advantage on platforms will vanish. This result is robust in different spatial network patterns. Conversely, when one of the platforms has a superior network structure of suppliers, its first-mover advantage will get strengthened, and it will achieve a better competition result; otherwise, its first-mover advantage will get weakened. These results provide an insight into the platform competition mechanism and will help platforms to make corresponding competitive strategies.