In order to efficiently detect community structure in complex networks, community detection algorithms can be designed from the perspective of node similarity. However, the appropriate parameters should be chosen to achieve community division, furthermore, these existing algorithms based on the similarity of common neighbors have low discrimination between node pairs. To solve the above problems, a noval community detection algorithm using closeness similarity based on common neighbor node clustering entropy is proposed, shorted as CSCDA. Firstly, to improve detection accuracy, common neighbors and clustering coefficient are combined in the form of entropy, then a new closeness similarity measure is proposed. Through the designed similarity measure, the closeness similar node set of each node can be further accurately identified. Secondly, to reduce the randomness of the community detection result, based on the closeness similar node set, the node leadership is used to determine the most closeness similar first-order neighbor node for merging to create the initial communities. Thirdly, for the difficult problem of parameter selection in existing algorithms, the merging of two levels is used to iteratively detect the final communities with the idea of modularity optimization. Finally, experiments show that the normalized mutual information values are increased by an average of 8.06% and 5.94% on two scales of synthetic networks and real-world networks with real communities, and modularity is increased by an average of 0.80% on the real-world networks without real communities.