Community structure is one of the most fundamental and important topology characteristics of complex networks. The research on community structure has wide applications and is very important for analyzing the topology structure, understanding the functions, finding the hidden properties, and forecasting the time-varying of the networks. This paper analyzes some related algorithms and proposes a new algorithm—CN agglomerative algorithm based on graph theory and the local connectedness of network to find communities in network. We show this algorithm is distributed and polynomial; meanwhile the simulations show it is accurate and fine-grained. Furthermore, we modify this algorithm to get one modified CN algorithm and apply it to dynamic complex networks, and the simulations also verify that the modified CN algorithm has high accuracy too.