Voxels are an effective approach to 3D mesh and point cloud classification because they build upon mature Convolutional Neural Network concepts. We show however that their cubic increase in dimensionality is unsuitable for more challenging problems such as object detection in a complex point cloud scene. We observe that 3D meshes are analogous to graph data and can thus be treated with graph signal processing techniques. We propose a Graph Convolutional Neural Network (Graph-CNN), which enables mesh data to be represented exactly (not approximately as with voxels) with quadratic growth as the number of vertices increases. We apply Graph-CNN to the ModelNet10 classification dataset and demonstrate improved results over a previous graph convolution method.