Due to the diversified demands of quality of service(QoS) in volume multimedia application, QoS routings for multiservice are becoming a research hotspot in low earth orbit(LEO) satellite networks. A novel QoS satellite routing algorithm for multi-class traffic is proposed. The goal of the routing algorithm is to provide the distinct QoS for different traffic classes and improve the utilization of network resources. Traffic is classified into three classes and allocated priorities based on their QoS requirements, respectively. A priority queuing mechanism guarantees the algorithm to work better for high-priority classes. In order to control the congestion, a blocking probability analysis model is built up based on the Markov process theory. Finally, according to the classification link-cost metrics, routings for different classes are calculated with the distinct QoS requirments and the status of network resource. Simulations verify the performance of the routing algorithm at different time and in different regions, and results demonstrate that the algorithm has great advantages in terms of the average delay and the blocking probability. Meanwhile, the robustness issue is also discussed.