Performing 3-dimensional computer-aided design (3D-CAD) model classification , retrieval, and reuse is of vital importance in industrial manufacturing, as it considerably shortens the engineering development cycle and reduces development costs. Although existing 3D model classification and retrieval methods achieve satisfactory performance when operating on meshes or point clouds, they cannot be applied directly to 3D-CAD models, which are generally represented by the boundary representation (B-rep). To address this issue, and to fully exploit the topology of B-rep, a graph structure descriptor called B-rep graph is proposed to pre-process B-rep data, and to extract the precise topological and geometric features from 3D-CAD models. Meanwhile, a novel efficient neural network called FuS-GCN, based on graph convolutional networks (GCNs), is designed to handle this graph data. To better extract the graph features and to improve the effect of pooling, the self-attention mechanism and feature fusion are incorporated into the pooling layer, yielding the proposed fusion self-attention graph pooling (FuSPool) algorithm. Finally, we demonstrate the effectiveness of FuS-GCN on 3D-CAD model data, while outperforming alternative 3D shape descriptors such as point clouds, voxels, and meshes.