Abstract: Exploring local community structure is an appealing problem that has drawn much recent attention in the area of social network analysis. As the complete information of network is often difficult to obtain, such as networks of web pages, research papers and Facebook users, people can only detect community structure from a certain source vertex with limited knowledge of the entire graph. The existing approaches do well in measuring the community quality, but they are largely dependent on source vertex and putting too strict policy in agglomerating new vertices. Moreover, they have predefined parameters which are difficult to obtain. This paper proposes a method to find local community structure by analyzing link similarity between the community and the vertex. Inspired by the fact that elements in the same community are more likely to share common links, we explore community structure heuristically by giving priority to vertices which have a high link similarity with the community. A three-phase process is also used for the sake of improving quality of community structure. Experimental results prove that our method performs effectively not only in computer-generated graphs but also in real-world graphs.