In this work we propose an algorithm for compressing the geometry of a 3D point cloud (3D point-based model). The proposed algorithm is based on the hierarchical clustering of the points. Starting from the input model, it performs clustering to the points to generate a coarser approximation, or a coarser level of detail (LOD). Iterating this clustering process, a sequence of LODs are generated, forming an LOD hierarchy. Then, the LOD hierarchy is traversed top down in a width-first order. For each node encountered during the traversal, the corresponding geometric updates associated with its children are encoded, leading to a progressive encoding of the original model. Special efforts are made in the clustering to maintain high quality of the intermediate LODs. As a result, the proposed algorithm achieves both generic topology applicability and good ratedistortion performance at low bitrates, facilitating its applications for low-end bandwidth and/or platform configurations.