Community structure is the key aspect of complex network analysis and it has important practical significance. While in real networks, some nodes may belong to multiple communities, so overlapping community detection attracts more and more attention. But most of the existing overlapping community detection algorithms increase the time complexity in some extent. In order to detect overlapping community structures in complex network more effectively, we propose a novel overlapping community detection method by local community expansion called OCDLCE. The proposed algorithm firstly partitions the network into small local communities using the local structural information, and then merges these communities to the final overlapping community structures. We present the concept of community connectivity as the criterion of community combination in the second stage of the proposed algorithm. The experimental results on both synthetic and real networks demonstrate that our algorithm improves the community detection performance, and at the same time, its time efficiency is better than the state-of-theart methods.