Low earth orbit satellite laser communication has become an important part of communications due to its large capacity and low latency. The lifetime of the satellite mainly depends on the recharge and discharge cycles of the battery. The low earth orbit satellites frequently recharge under sunlight and discharge in the shadow, which leads satellites to age quickly. This paper studies the energy-efficient routing problem for satellite laser communication and builds the satellite ageing model. Based on the model, we propose an energy-efficient routing scheme based on the genetic algorithm. Compared with shortest path routing, the proposed method improves the satellite lifetime by about 300%, and the performances of the network are only slightly degraded, the blocking ratio increases by only 1.2%, and the service delay increases by 1.3 ms.