Classification of objects from 3-D point clouds has become an increasingly relevant task across many computer-vision applications. However, few studies have investigated explainable methods. In this article, a new prototype-based and explainable classification method called eXplainable point cloud classifier (XPCC) is proposed. The XPCC method offers several advantages over previous explainable and nonexplainable methods. First, the XPCC method uses local densities and global multivariate generative distributions. Therefore, the XPCC provides comprehensive and interpretable object-based classification. Furthermore, the proposed method is built on recursive calculations, thus, is computationally very efficient. Second, the model learns continuously without the need for complete retraining and is domain transferable. Third, the proposed XPCC expands on the underlying learning method explainable deep neural networks (xDNN), and is specific to 3-D. As such, the following three new layers are added to the original xDNN architecture: 1) the 3-D point cloud feature extraction, 2) the global compound prototype weighting, and 3) the SoftMax function. Experiments were performed with the ModelNet40 benchmark, which demonstrated that XPCC is the only one to increase classification accuracy relative to the base algorithm when applied to the same problem. In addition, this article proposes a novel prototype-based visual representation that provides model- and object-based explanations. The prototype objects are superimposed to create a prototypical class representation of their data density within the feature space, called the compound prototype cloud. They allow a user to visualize the explainable aspects of the model and identify object regions that contribute to the classification in a human-understandable way.