Satellite networks are drawing more and more attention, since they can provide various services to everywhere on the earth. Communication devices in satellites are typically powered by solar panels and battery cells, which are carefully designed to guarantee power supply and avoid deficiency. However, we find that unrestrained use of energy will cause a satellite to age quickly, because the number of recharge/discharge of battery cells is limited. Due to the extremely high cost of satellites, the development of energy-efficient satellite routing to save energy and prolong satellite lifetimes has become significantly important. In this paper, we do comprehensive studies. First, we model the power consumption of a space router, power supply by solar panels, and aging of battery cells formally. Second, we define the energy-efficient satellite routing (EESR) problem, and prove that the EESR problem is NP-hard. Then, we develop three algorithms to gradually solve the EESR problem. GreenSR-B is a baseline algorithm which computes link costs iteratively to compute a routing that minimizes the total recharge/discharge cycle number. GreenSR-A selects space routers to switch into sleep mode to improve energy conservation. GreenSR jointly considers energy efficiency and QoS requirements of path length and the maximum link utilization ratio. We evaluate our algorithms by simulations on a low earth orbit satellite network with real Internet usage traces. The results show that GreenSR can prolong the lifetime of satellite battery cells by more than 40%, with little increment in path length and a small link utilization ratio.