Aiming at the Wireless Sensor Networks(WSNs) of Duty Cycle(DC), the researchers have attempted to reduce transmission delay and energy consumption by Anycast technology, and have conducted in-depth research. An Energy Efficient Anycast Routing(EEAR) protocol is proposed in this paper. EEAR adopts a new Anycast routing metric called Expected Energy Consumed(EEC) that is contrary to previous Anycast routing metrics. By using the new Anycast routing metric, the forwarder set is selected reasonably and the expected energy consumed can be minimized along the path of a packet. Simulation results show that EEAR consumes less energy than similar existing protocols, while maintaining a comparable delay and high delivery rate.