Real-world network nodes contain a large number of attribute information and there is an overlapping characteristic between communities. Aiming at the problems, an overlapping community detection algorithm for attributed networks was proposed. The network topology structure and node attributes were fused to define the intensity degree and interval degree of network nodes, which were designed to describe the characteristics of community-the dense interior connection and the sparse exterior connection respectively. Based on the idea of density peak clustering, the local density centers were selected as community centers. On this basis, an iteration calculating method for the membership of non-central nodes about each community was proposed, and the division of overlapping communities was realized. The simulation experiments were carried out on real datasets. The experimental results show that the proposed algorithm has better performance in community detection than LINK algorithm, COPRA algorithm and DPSCD (Density Peaks-based Clustering Method).