To address the problem that existing networks find it difficult to learn local geometric information of point cloud effectively, a graph convolutional network that fuses multi-resolution features of point cloud is proposed. First, the local graph structure of the point cloud is constructed by the k-nearest neighbor algorithm to better represent the local geometric structure of the point cloud. Second, a parallel channel branch is proposed based on the farthest point sampling algorithm, which obtains point clouds with different resolutions by downsampling them and then groups them. To overcome the sparse characteristics of the point cloud, a geometric mapping module is proposed to perform normalization operations on the grouped point cloud. Finally, a feature fusion module is proposed to aggregate graph features and multi-resolution features to obtain global features more effectively. Experiments are evaluated using ModelNet40, ScanObjectNN, and ShapeNet Part datasets. The experimental results show that the proposed network has state-of-the-art classification and segmentation performance.