This paper takes advantage of the universal power-law distribution of social networks and proposes a leader based local community detection algorithm EALCN. It uses local structural information in the network to optimize a local objective function. A local community can be detected through continuous optimization of the function by expanding from an initial core member computed by a modified PageRank sorting algorithm. The advantage of this algorithm is that it only uses some local information of the network to detect communities by utilizing highly important nodes. The efficiency is higher than traditional algorithm