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Satellite networks can provide worldwide-coverage wireless data gram services, but cause great challenges for how to efficiently route data gram. The Low Earth Orbit (LEO) satellite is becoming an essential part of the Next-Generation internet with short round-trip delay and low power consumption. In this paper, we propose a routing algorithm for LEO satellite constellation networks with high performance. It needs less memory and computer power, but is capable of highly efficient data gram route. Through simulation we demonstrate the performance of the proposed algorithm. Moreover, we integrate the IP protocol into the algorithm to prove its deploy ability.