A routing algorithm named Sub-Game Energy Aware Routing (SGEAR) modeled by Dynamic Game Theory is proposed in this paper to make better routing choices. SGEAR takes the residual energy of the nodes and the energy consumption of the path into consideration and achieves Nash Equilibrium using Backward Induction. Compared with Energy Aware Routing, SGEAR can provide stable routing choices for relaying nodes and the energy of the network can still burn evenly. Moreover, this algorithm is more suitable for being combined with sleeping scheduling scheme and thus prolongs the lifetime of Wireless Sensor Networks. Simulation results show that, combined with sleeping scheduling scheme, SGEAR has an increase of 20% in energy saving compared with Energy Aware Routing.