In this paper, we propose a Height-Aware Graph Convolution Network (HA-GCN) to solve the challenging problem of Airborne laser scanning (ALS) point cloud classification. For samples with uneven distribution and large differences in scale, classification using local features is unstable and easily affected by noise. Therefore, we use a multi-layer stacked Edge Convolution (EdgeConv) operators to extract local and global information at the same time. In addition, in view of the characteristics of the height distribution of airborne LiDAR point cloud, we introduce height attention weights as a supplement to feature extraction. First, the original point cloud is divided into sub-blocks and sampled to a fixed number of points. Then, the EdgeConv operator is used to extract local-global features. At the same time, the Height-Aware (HA) module is used to generate attention weights. Finally, the height attention weights are applied to the feature extraction network and the classification is completed after post-processing. The experimental results on the Vaihingen dataset show that the proposed method achieves the effect of the state-of-the-art methods in overall accuracy, as well as impressive results in single-category classification accuracy.