Abstract: These recent years, Low Earth Orbit (LEO) satellite networks, which have global coverage and short round-trip delays, have been playing an increasingly important role. As fast speed, frequent handover and time-varying topology, to develop specialized and efficient routing algorithm is a huge challenge in LEO satellite networks. A Distributed Routing Algorithm with Traffic Prediction (TPDRA) is proposed in this study. TPDRA solves the linearly inseparable problem of satellite traffic prediction in higher dimensionality space and finds the optimal path for data packets through mobile agents. TPDRA consists of two parts, traffic prediction and routing decision. In traffic prediction module, the upcoming traffic from terrestrial is forecasted using Radial Basis Function neural network. In routing decision module, mobile agents traverse the whole satellite networks and collect the routing information. The final routing decision factor is not only depending on the current state of satellite networks, but also related to the future state of satellite nodes. Simulation shows that, compared with ACO, TPDRA has better transmission delay as well as intensive performance for congestion.