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One critical issue for routing in mobile ad hoc networks (MANET) is how to select a stable path that can last longer since mobility may cause radio links to break frequently. In this paper, a link stability prediction model is proposed firstly, it uses the relative motion and the distance between two neighbor nodes to evaluate the mean link duration, which is used to predict link stability. Then a link stability prediction-based routing (LSPR) algorithm is proposed. In LSPR algorithm, the mid-nodes forward RREQs after delay which is decided by the mean link duration predicted. Furthermore a forwarding rule which can reduce the number of RREQs forwarded by receding neighbor nodes is designed. Taking advantage of simulation, LSPR algorithm is compared with AODV routing algorithm and other two stability-based routing algorithms. The simulation results show that LSPR algorithm is better than other three routing algorithms, and can improve route stability and network performance effectively.