In mobile ad hoc networks (MANETs), node mobility causes network topology to change dynamically over time, which complicates such important tasks as routing. The previous stability-oriented routing algorithms usually focus on how to discover a stable route, but rarely consider the adaptability of constructed route to the change of node's motion. In this paper, a stability-enhanced routing for mobile ad hoc networks is proposed. In the proposed routing algorithm, the link expiration time (LET), which is used to assess the stability of link, is calculated accurately in company with the discovery of some available stable routes in reactive manner. Then the asynchronous mobility information mechanism is introduced to make the stability of current route can adapts to node's motion. Based on the updated LET, the discovery of alternative stable route is determined, which can ensure the continuous transmission of data. Simulation results indicate that the proposed stability-enhanced routing scheme can improve network performance effectively.