Abstract: A measure of local community structure was defined, and an mining algorithm of local community structure based on the minimal increment of link degree of a community was presented for resolving the time complexity problems of finding local community structure in complex networks. The algorithm ran in time O (kd) for general graphs, where d is the mean degree and k is the number of vertices to be explored. In order to determine its performance and calculation precision, the algorithm was compared with the classical local community identification approach, Clauset algorithm. Experimental results show that mining results of the algorithm are as effective as those of Clauset algorithm on the whole, and the algorithm is much faster than Clauset algorithm.