Abstract: Satellite networks provide global coverage and support a wide range of services; in particular, Low Earth Orbit (LEO) satellites are becoming more and more important for their short round trip delays. One of the challenges in LEO satellite network research is to develop a specialized and efficient routing algorithm. In this paper, the researches that have been done in the passed ten years are reviewed, and a simple and efficient routing algorithm (On-Demand Partial Topology Routing Algorithm) is proposed. This algorithm guarantees the routes have the minimum delay while having a good convergence time which make the algorithm suitable for the dynamic topology of LEO satellite networks. Then, the performance of the algorithm is evaluated through simulation and future works are also proposed.