In most mobile ad hoc networks (MANETs) clustering protocols, the clusterhead nodes take on a special role in managing routing information. However, the frequent changes of the clusterheads affect the performance of the routing protocol. Eventually, the clustering stability in MANETs would be significantly affected. The route between two nodes changes constantly as the clusterhead set changes. Stability therefore can be an important element in the design of routing protocols. In this paper, we propose a new routing algorithm called Grid-based Stable Backup Routing Algorithm (GSBRA). GSBRA will divide the network into small grid zone. GSBRA utilizes primary grid head (PGH) chains and backup grid head (BGH) chains to route data. The BGH works as a backup for the PGH and is the future leader for the grid. The primary route can be established through the PGHs, while the backup route can be established through the BGHs. Consequently it will improve the network lifetime. It is evident from simulation results that comparison with on-demand routing protocols (AODV-BR and AODV), GSBRA has a higher average route lifetime, higher packet delivery ratio and lower routing load because GSBRA can provide robustness to mobility.