To address the issues of uneven satellite network load and unstable link connections, a globally adaptive satellite network routing strategy based on traffic prediction (G-AODV) is proposed by enhancing the existing Ad hoc On-Demand Distance Vector Routing (AODV) protocol. To prevent heavily loaded nodes from becoming intermediate nodes, G-AODV introduces a traffic prediction mechanism in the route discovery phase. The routing request packet adopts the corresponding forwarding control policy based on the comparison between the predicted traffic load value at the next moment and the dynamic threshold. At the same time, a path replacement strategy is adopted to replace paths before node congestion occurs to achieve load balancing. Considering the unstable characteristics of the satellite chain that easily breaks, the route maintenance phase selects a path repair method by judging the node stability to avoid secondary breaks in the route. The simulation results show that in scenarios with different packet delivery rates, compared with the three comparative routing strategies, the packet delivery rate of G-AODV is increased by up to 20%, the packet loss rate is reduced by 22%, and the end-to-end delay is significantly reduced. In scenarios with different communication connection pairs, G-AODV鈥檚 packet delivery rate increased by up to 20%, the packet loss rate decreased by 18%, and the end-to-end delay was still reduced.