Opportunistic network is a type of tolerant delay network (DTN). Establishing routing path from the source node to the destination node may not be possible. So the traditional routing algorithms are not suitable for this network except the Epidemic. But due to its replication characteristics, the energy of node will be used up quickly. Many researchers have achieved lots of results on how to forwarding data strategically in Epidemic, but pay little attention to the energy consumption of nodes. This paper proposes an energy-saving algorithm named ERSE which combines the asynchronous sleep mechanism. The ERSE is based on the node communication model, making the node enter the sleeping state when it's not active. It also controls the sleep duration dynamically to ensure that the node does not miss the communication opportunities. ERSE makes the low-energy state nodes enter a forced sleeping state at the same time to avoid them going to use up their energy quickly. The simulation results show that ERSE routing algorithm can greatly save the energy consumption of nodes.