Abstract: To resolve the channel resources waste problem of the typical source-based multicast routing algorithm in low earth orbit (LEO) satellite networks, a new core-based shared tree algorithm called the core-cluster combination shared tree (CCST) algorithm and its improved one (i.e. w-CCST algorithm) were proposed. The (w-)CCST algorithm consists of the dynamic approximate center (DAC) core selection method and the (weighted) core-cluster combination multicast routing construction method. The core-cluster combination method takes core node and its nearest group member in hops as initial core-cluster, and extends it to construct entire multicast tree step by step by a shortest path scheme between newly-generated core-cluster and surplus group members, which can greatly improve transport bandwidth utilization. In the w-CCST algorithm, a weighted factor was proposed to decrease end-to-end propagation delay and meanwhile increase tree cost a bit to support some real-time applications with strict delay requirements. Simulation results show that tree cost performance of the CCST algorithm is greatly better than that of other algorithms, while end-to-end propagation delay performance of the w-CCST algorithm is better than that of the CCST algorithm.