The dynamics of Mobile Ad-hoc NETworks (MANETs), as a consequence of mobility of mobile hosts, pose a problem in finding stable multi-hop routes for communication between a source and a destination. Traditional ad-hoc routing protocols are proposed to find multi-hop routes based on shortest path routing algorithms, which cannot effectively adapt to time-varying radio links and network topologies of MANETs. In this paper, a novel stability-based ad hoc routing protocol, which is named as Ad-hoc On-demand Stability Vector (AOSV) routing protocol, is proposed to properly and effectively discover stable routes with high data throughput and long lifetime by considering the radio propagation effect on signal strength. Here, a stochastic mobile-to-mobile radio propagation model is proposed to predict path loss as well as received signal strength between adjacent nodes, and the estimation of link/route stability is derived from the prediction of signal strength. With awareness of link and route stabilities, a path finding algorithm is designed to explore the stable route with largest route stability for a source and destination pair. The performance of AOSV protocol is compared with the well-known Ad-hoc On-demand Distance Vector (AODV) routing protocol and other related works. Simulation results indicate that the AOSV routing protocol leads to significant throughput increases up to 70% improvement comparing to AODV, and provides better performance than related works.