Energy-aware routing is important in multi-hop wireless networks that are operated by battery power, e.g., wireless sensor networks. To maximize the network survivability, the energy efficiency of paths must be taken into account for route selection. Simple heuristics such as choosing paths with minimal energy consumption do not perform well, because the energy of the nodes on such paths may deplete quickly. The issue is particularly serious for the networks with regular traffic pattern as in monitoring sensor applications. Existing solutions to this issue typically adopt the multi-path routing approach, in which multiple paths are set up between source and destination and one (or all) of the paths is (are) used at a certain moment. However, this approach involves high overhead for establishment and management of multiple paths. In this paper, we present a static single-path routing algorithm which uses one energy-efficient path for each communicating peer throughout the network lifetime, eliminating the overhead of multi-path routing. It is proved that our algorithm achieves a constant factor approximate of the optimal solution. We compare the performance of the proposed scheme with that of multi-path routing via simulations. Despite the use of single static path, the proposed scheme outperforms the dynamic multi-path approach, particularly under heavy network loads.