"Mobile Ad Hoc Network" (MANET) is composed of a set of wireless mobile nodes, it is a self-organized environment which does not need any infrastructure. The topology of this type of network is formed dynamically and the mobility feature of the nodes causes rapid, unpredictable and frequent network topology changes. All nodes in this network are mobile in nature and driven by batteries, that could cause link breakage if a battery of a node goes empty. Rapid topology change and the limited resources in these networks made designing an efficient routing protocol a challenging problem. In this paper, we propose a new route discovery scheme of AODV that reduces routing overhead, prolong route life time, and relatively minimum hop counts. The suggested scheme is called EDA- AODV, where the route is selected using two main metrics: node energy factor and node distance from its transmitting predecessor node. The proposed scheme has been implemented using network simulator (NS2. Ver.2.31). The emulation results indicate that, the performance of EDA-AODV outperforms the original AODV from point of view: throughput, number of alive nodes, normalized routing load and overall hop count.