Since Low Earth Orbit (LEO) satellites provide short round trip delays, they are becoming increasingly important for real-time applications such as voice and video traffic. Several strategies have been proposed for routing in a LEO satellite system. Some of them are based on the Internet Protocol (IP), the Asynchronous Transfer Mode (ATM) switching, and the Routing Sets (RS).This paper will introduce an improving for the new packet routing mechanism over inter-connected satellite networks that is the Minimum Flow Maximum Residual (MFMR) algorithm that will be based on RS concept and will give simulation results of a certain scenario. Our proposed algorithm is based on the Hybrid mesh topology (one of many mesh topologies used in LEO satellite routing). The algorithm is developed and implemented using a software simulation in Matlab. The proposed algorithm tries to minimize the maximum flow over a given set of shortest paths from the source to destination, and also, generates minimum propagation delay paths. The propagation delay we get is less than that of MFMR algorithm, i.e., improving the performance of the LEO satellite network by using Hybrid topology.