A hierarchical overlapping community discovery algorithm based on node purity (OCFN-PN) is proposed in the paper. This algorithm chooses the maximal relative centrality as the initial community, which solves the problem of inconsistent results of the community discovery algorithm based on fitness resulting from randomly choosing nodes. Before optimizing and merging communities, the community overlapping degree and the joint-union should be calculated so that the problems of twice merging can be solved. Research results show that this algorithm has lower time complexity and the communities obtained by this algorithm are more suitable for real world networks.