Abstract: When we design the topology,how to assign the numerable communication terminals on each satellite to build communication links,and then construct a well performing network topology,becomes a significant research problem. With the object of minimizing the average distance between lunar relay satellites to ground station, and subject to the communication terminal quantity on satellites as well as the connectivity between lunar relay satellites and ground station,we proposed the link assignment algorithm based on competitive decision(LAA-CD)and the link assignment algorithm based on simulated annealing (LAA-SA),and then compared the performances of those two algorithms with the greedy algorithm. The simulation result shows that both resulted topologies of LAA-CD and LAA-SA have shorter average distance than the greedy algorithm,and LAA-SA can greatly reduce the time complexity. This paper further compares two different constellations and finds out the network topology based on the lunar polar orbit satellite constellation always has a shorter average distance than the Earth-Moon Lagrange satellite constellation. It will provide technology support for the future satellite networks assignments.