Abstract This paper focuses on solving the routing optimization problem under the dynamic topology of the satellite communication network. With the rapid development of low-earth-orbit (LEO) satellite network communication technology, the dynamically changing topology of satellite networks has brought about frequent link switching and triggered a large number of routing updates. This paper proposes an improved routing algorithm named the Stable A-Star Routing (SASR) algorithm. The SASR algorithm is based on the A-star algorithm and aims to reduce path-switching frequency and enhance path stability by optimizing the path selection strategy. Through detailed simulation experiments and performance evaluation, we verified the performance advantages of the SASR algorithm in terms of the number of path switches, the number of path hops, the route convergence time, and the occurrences of congestion in business under different business volumes, and conducted comparative studies with classic algorithms. The results show that the SASR algorithm offers obvious advantages in key performance indicators. Compared with the Dijkstra algorithm and the A-star algorithm, the average number of path switches can be reduced by 22% and 10%, respectively. It shows more prominent advantages under a larger business volume, providing an efficient and reliable solution for routing optimization under the dynamic topology of satellite communication networks.