Point clouds are among the popular geometry representations in 3D vision. However, unlike 2D images with pixel-wise layouts, such representations containing unordered data points which make the processing and understanding the associated semantic information quite challenging. Although a number of previous works attempt to analyze point clouds and achieve promising performances, their performances would degrade significantly when data variations like shift and scale changes are presented. In this paper, we propose 3D graph convolution networks (3D-GCN), which uniquely learns 3D kernels with graph max-pooling mechanisms for extracting geometric features from point cloud data across different scales. We show that, with the proposed 3D-GCN, satisfactory shift and scale invariance can be jointly achieved. We show that 3D-GCN can be applied to point cloud classification and segmentation tasks, with ablation studies and visualizations verifying the design of 3D-GCN.