PointNet is one of the representative research results obtained from three-dimensional point cloud classification, which innovatively employs a deep learning model for point cloud classification and achieves good results. However, PointNet does not capture local information of each point, and it considers only the global features of point clouds. Herein, we propose a model for point cloud classification based on graph convolutional networks to solve this problem, in which a k-nearest neighbor (kNN) graph layer is designed and plugged into a PointNet model. The local information of point clouds can be effectively obtained by constructing the kNN graph layer in the point cloud space, which can improve the accuracy of point cloud classification. The point cloud classification experiment is conducted on the ModelNet40 dataset, and the effects of the different neighbor values of k on the output accuracy are compared. The results demonstrate that the highest classification accuracy is achieved when k is 20, reaching 93.2%, which is 4.0% higher than that of PointNet.