This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods to yield a density-based hierarchical clustering algorithm. We first formally define the types of clusters DP and DBSCAN are designed to detect; and then identify the kinds of distributions that DP and DBSCAN individually fail to detect all clusters in a dataset. These identified weaknesses inspire us to formally define a new kind of clusters and propose a new method called DC-HDP to overcome these weaknesses to identify clusters with arbitrary shapes and varied densities. In addition, the new method produces a richer clustering result in terms of hierarchy or dendrogram for a better understanding of cluster structures. Our empirical evaluation results show that DC-HDP produces the best clustering results on 28 datasets in comparison with 8 state-of-the-art clustering algorithms.