A point cloud classification method based on graph convolution and multilayer feature fusion is proposed to solve the problem that the existing deep learning point cloud classification methods are insufficient for local feature mining and to improve the quality of feature fusion at different levels. First, the K-neighborhood graph is constructed, the improved edge function is used to extract more fine-grained edge features, and the aggregation method based on attention mechanism is used to obtain more representative local features. Next, the multilayer feature fusion module adjusts the channel weight of the intermediate features, introduces residual connection to fuse the features of different levels, and deepens the information transmission between the network layers. The experimental results using the standard public dataset ModelNet40 show that the proposed method exhibits better classification performance than other point cloud classification methods. The proposed method is robust and has an overall classification accuracy of 93.2%.