In order to implement global precision navigation, the global navigation satellite system must rely on information exchange with the ground station to achieve system time synchronization and inter-satellite ranging. For the limitations of ground stations located in territory and actual communication requirements, it is essential to study the routing problem of navigation satellite network, which indicates that traditional routing technology cannot meet the requirements of global navigation satellite system. Aiming to control the dynamic topology of global navigation satellite system and satisfy communication constraints, we investigate the topology-adapting strategy for inter-satellite link constructing and routing. First, we propose the design method of the inter-satellite link scheme based on fixed topology to satisfy the requirements for delay and relay hops. Then, we build the constraint programming model of the global navigation satellite system routing problem. In further, we design the routing calculation framework and optimization strategies to enhance the routing performance of the transmission scheme. Through the simulation and numerical results, we demonstrate that the fixed topology scheme can meet the navigation requirements, and the proposed strategy can effectively improve the routing performance.