Community mining is an important work in complex network analysis, and many algorithms have been proposed. However, most of them are based on the links to find the cohesive community structure. Taking the nodes that have different behaviors and influences in real-world networks into consideration, together with links between nodes, a two?stage community mining algorithm based on central maximal-clique expansion is proposed. In the first stage, initial communities are found: Firstly, all the cohesive cliques are found out in the network, and then [k] separate cohesive and influential central maximal-cliques are chosen to form initial communities. In the second stage, the final community division is detected: For the nodes outside the initial communities, taking potential impacts of neighbor nodes into consideration, the neighbor nodes are expanded to the corresponding connected closely community by adopting the local modularity. Experimental results show that the method can quickly reveal cohesive community structure in network, compared with the FN algorithm it has a relatively higher accuracy and modularity, compared with the GN algorithm, it do not need to know the prior number of communities.