Abstract The density-peak clustering (DPC) method (Rodriguez and Laio, 2014) clusters the data efficiently by fast searching density peaks. Recently, an improved DPC algorithm named 3DC method (Liang and Chen, 2016) was proposed for automatically detecting the correct structure of the clusters. However, it is difficult to select correct parameters for the DPC and 3DC methods and the local property of data set can’t be revealed due to their global density assumption in some scenarios. To overcome this drawback, the K-nearest neighbor (KNN) framework is adapted for defining the density of the DPC method. Nevertheless, such KNN-based methods can’t automatically detect the number of the clusters compared with the 3DC method. In this paper, an automatic clustering method is proposed, which needs only a discrete input parameter. Meanwhile, by utilizing the cluster stability for the Chameleon framework, the proposed method can automatically detect the correct structure of the clusters. The experimental results on the synthetic and real world data demonstrate that the proposed method has a more robust performance. Besides, the proposed method is robust to the choices of the input parameter.