In mobile ad hoc networks (MANET), node movement often makes the wireless link break, and results in the routing invalidation. In order to improve the stability of routing, based on the analysis of the time-t holding probability of single link, an on-demand routing protocol is provided based on the time-t holding probability of a whole path. With double reply of routing request from destination and reverse optimizing of middle nodes, this protocol chooses the path that has the maximal time-t holding probability as the best routing. Simulations show that, compared with AODV (ad hoc on-demand distance vector) and DSR (dynamic source routing), this protocol saves the overhead of the protocol and reduces the end-to-end delay of the packet.