A mobile ad hoc network (MANET) is an infrastructureless and highly dynamic network. Routes in such a network may fail frequently because of node mobility or other issues. Stability therefore can be an important element in the design of routing protocols. Stable routes, also called the long-lived routes, can be discovered and used to reduce the overhead resulted from route maintenance in ad hoc networks. In this paper we propose the Long-lived Route Prediction (LRP) scheme to discover stable routes. The LRP scheme is distributed, and it predicts the long-lived routes based on the history of link lifetime. Furthermore, we apply the LRP scheme to both open area and urban area using simulation. Simulation results show that the LRP scheme can indeed discover stable routes to reduce the number of route rediscovery, and can be much more efficient and scalable.