This paper presents a feature reasoning-based graph convolution network (FR-GCNet) to improve the classification accuracy of airborne multispectral LiDAR (MS-LiDAR) point clouds. In the FR-GCNet, we directly assign semantic labels to all points by exploring representative features both globally and locally. Based on the graph convolution network (GCN), a global reasoning unit is embedded to obtain the global contextual feature by revealing spatial relationships of points, while a local reasoning unit is integrated to dynamically learn edge features with attention weights in each local graph. Extensive experiments on the Titan MS-LiDAR data showed that the proposed FR-GCNet achieved a promising classification performance with an overall accuracy of 93.55%, an average F1-score of 78.61%, and a mean Intersection over Union (IoU) of 66.78%. Comparative experimental results demonstrated the superiority of the FR-GCNet against other state-of-the-art approaches.