Since nodes in the mobile ad hoc networks (MANETs) network move freely and randomly, routes often get disconnected. The major challenge for MANETs is therefore to implement routing protocols that must respond to changes in the network topology in order to maintain and reconstruct the routes in a timely manner as well as to establish reliable routes. In this paper, we propose a new routing algorithm called Grid-based Stable Routing Algorithm (GSRA). GSRA exploits the concept of a routing protocol called GRID. The main difference between these two protocols is that GSRA considers grid head stability and route stability but the GRID does not. In GSRA, grid partitioning is the same as in the GRID routing protocol. Each grid zone selects a grid head to route. Also, GSRA defines a new parameter called grid head stability to select stable grid head. In routing discovery, each node receives the RREQ packet and uses the link stability metric to evaluate link stability. The destination node collects several feasible routes and then selects the most stable route according to end-to-end reliability. Simulation results indicate that GSRA has a higher packet delivery ratio, lower end-to-end delay and lower routing load than GRID and AODV.