Recently, satellite networks are widely used for communication in areas lack of network infrastructures, and will act as the backbones in the next generation internet. Therefore, the availability of satellite networks is very important. In space, the energy is always limited for satellites, and highly efficient energy utilization would certainly improve the availability of satellite systems. In this paper, we consider the energy-saving optimization for the LEO satellite network instead of a single satellite. We modify and extend the multicommodity flow model [3] to switch off satellite nodes and links as much as possible in LEO satellite networks. Taking advantage of the multi-coverage scheme and traffic distribution patents in satellite networks, we improve the heuristic algorithms in [3] to turn off the unnecessary satellites, up-down links and inter-satellite links respectively up to 59 %, 61 % and 72 % under the constraints of link utilization and routing hops increase ratio, and the total energy saving ratio can be up to 65 %. Finally, the availability of LEO satellite networks has been deeply developed.