The defects of overlapping community detection algorithm COPRA based on multi-label propagation include instability and pre-parameter limits, this study proposed a multi-label propagation algorithm for overlapping community detection based on LeaderRank and the node similarity. The algorithm uses the LeaderRank algorithm to sort the nodes in the network to determine the order of nodes updating. Then, re-design the label update strategy according to the similarity of nodes to improve the stability of the algorithm. The algorithm is applied to the artificial network and the real networks. The experimental results show that the proposed algorithm has high accuracy and stability for detecting overlapping communities.