LEO satellite networks have many advantages, such as global coverage and short latency, which play a crucial role in the future global communications. Under the tide of the Internet of Things, LEO satellite networks, as an effective means of connecting remote regions, will become indispensable pillars in the integrated system of the Internet of Things. In LEO satellite communication systems, routing have always been a big challenge due to the relative motion of satellites. The K shortest route algorithm is a typical one of the routing algorithms that emerged in recent years. By calculating K shortest path routes, an optional route set is formed, and then the best route is determined by the route selection strategy. For the massiveness and suddenness of the IoT terminals, the original K Shortest path algorithm cannot balance the load, resulting in partial link congestion affecting the overall system performance. In this paper, the route selection strategy of K Shortest path is improved by the routing strategy of the algorithm, and the rerouting process is added. Under the Iridium constellation, the packet loss rate, throughput and delay of the shortest path algorithm after the improvement are analyzed. The results show that the improved algorithm can effectively reduce the packet loss rate and improve the link utilization and throughput of the system.