SimRank is a method based on the topological structure information of the graph to measure the similarity between any two objects. However， in real large-scale social networks， the iterative computation between nodes is time-consuming. Here we propose a hierarchical community detection algorithm based on global matrix smooth convergence using SimRank， called SGSC. First， the SGSC algorithm identifies the initial core nodes in a network by classical measurement.Then， it smoothly converges a matrix to calculate SimRank to obtain original core nodes. Based on the global convergence matrix， we cluster the communities around the core nodes and use a closeness index to merge two communities. By recursively repeating the process， a dendrogram of the communities is eventually constructed. We validate the performance of SGSC by comparing its results with those of two representative methods for three real-world networks with different scales， and comparison results show that the proposed SGSC algorithm improves the accuracy in community division and reduces running time in social networks of different scales.