3D object recognition and detection based on point clouds is an important research topic in the fields of computer vision and autonomous navigation. Nowadays, deep learning algorithms have greatly improved the accuracy and robustness of 3D point cloud classification. However, deep learning networks usually have problems such as complex network structure and time-consuming training. This study proposes a three-dimensional point cloud classification network named Point-GBLS, which combines deep learning and a broad learning system. The network structure is simple and the training time is short. Firstly, point cloud features are extracted by a deep learning-based feature extraction network. Then, an improved broad learning system is used to classify them. Experiments on the ModelNet40 and ScanObjectNN dataset show that the recognition accuracy of Point-GBLS is more than 92% and 78% respectively. The training time is less than 50% of that of similar deep learning methods. It is superior to deep learning networks with the same backbone.