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A new multicast routing algorithm, namely multiple-cores shared-tree (MCST), is proposed especially for low earth orbit (LEO) satellite IP networks. MCST can create a shared tree with multiple cores for each dynamic multicast group. And the outward extending searching square (OESS) approach is developed to select cores for multicast groups in the network, also core updating and dynamic management of group membership are supported in the algorithm. Simulation results show that MCST has good tree cost performance. In addition, MCST not only can balance traffic in the network, but it is robust by using multiple cores.