Aiming at the congestion problem caused by the uneven global traffic distribution in the LEO satellite network and the QoS guarantee problem caused by multiple communication services, a Multi-Service QoS Routing Algorithm based on Region Partition (MSR-RP), which considering the problem of funnel traffic caused by the limited distribution of gateways, is proposed in this paper. On the one hand, it reduces the number of regional nodes by dividing the dynamic area and lowers the overall calculation complexity of the algorithm; on the other hand, it uses the shortest path algorithm to calculate the route in the light-load region, and uses a multi-objective genetic algorithm to calculate the route in the heavy-load region. Through these two methods, the QoS of different traffic is assured and load balancing is achieved. The simulation and implementation of the MSR-RP routing algorithm, the designing of simulation scenarios, and the comparison of the performance of the TCD algorithm with the MSR-RP algorithm are also demonstrated. The results show that the MSR-RP algorithm has good load balancing performance while providing QoS guarantee, and the network throughput has been improved. With the increase of the overall traffic volume, the proposed algorithm has lower average network delay and packet loss rate than the TCD algorithm.