The performance of mobile ad hoc network (MANET) primitives such as routing and broadcast can be improved by the availability of a virtual backbone. It is known that computing the connected dominating set (CDS) is a viable solution to construct a virtual backbone in MANETs. Most of existing CDS protocols emphasize on the small size of CDS in which node identifier or number of neighbors is used as a node priority. Since energy constraint is the primary issue in resource-limited MANETs, the node priority should include the energy level at each node to prolong the life time of a CDS. To this end, we propose Energy-Aware Node Priority (EAP), where nodes with more energy has higher probability to be selected as backbone nodes. The proposed protocol not only prolongs the life time of CDS but also keeps the size of a CDS competitive. The simulation results validate that our scheme outperforms the existing energy-aware CDS protocols.