As the core of routing protocols, route selection algorithm plays the key role in the scenario of quick mutability of the network topology. In mobile ad hoc networks, node mobility has been one of the dominant factors which cause the loss of performance so that the path duration and stability has to be taken into account. On the other hand, energy awareness for computation is becoming another crucial parameter. In this paper, a novel routing selection algorithm has been proposed without any additional device (such as GPS). Path stability based on stability change ratio and energy awareness has been jointly considered in this proposed algorithm. In order to verify the correctness of the proposed solution an enhanced routing protocol based on AODV named EN-AODV has been presented. Simulation results show that the performance of EN-AODV is better than that of traditional AODV and NCR-AODV in terms of normalized routing load, packet delivery ratio and nodes death rate.