Node mobility is one of the dominant factors causing decreased performance in mobile ad hoc networks and restricting network scalability. Selecting stable paths is an effective way to reduce the impact of node mobility. Current methods of selecting stable paths in mobile ad hoc networks suffer from several shortcomings. They may need a hardware function support for geographical position location or cross-layer function support for sending signal strength information to upper layers. In this paper, a new method of selecting stable paths based on the neighbor change ratio is proposed. Neither the special hardware support nor the cross-layer support is needed in this new method. NCR-AODV (neighbor change ratio Ad hoc on-demand distance vector) routing protocol is an extension of the AODV (Ad hoc on-demand distance vector) on-demand route protocol with the new method. The new protocol selects the path which has smaller hop counts and less local topology changes to forward data. The simulation results show that NCR-AODV protocol decreases the long path break probability and improves the network performance.