Lifetime-maximization is the critical concern for wireless sensor networks (WSNs). We notice that two common issues in existing routing schemes for WSNs are that (1) a path may traverse through a fixed set of sensors, draining out their energy quickly, and (2) packet retransmissions over an unreliable link of any fixed-path may consume energy significantly. In this paper, we exploit two natural advantages of opportunistic routing, i.e., path diversity and the improvement of transmission reliability, to develop a distributed routing scheme (called EFFORT) for prolonging the network-lifetime of a WSN. Specifically, a new metric is proposed to assist each sensor in determining a suitable set of forwarders as well as their priorities and, thus, enables EFFORT to extend the network-lifetime. Simulation results show that EFFORT effectively achieves network-lifetime extension compared to other routing protocols.