Since the point cloud data is inherently irregular and unstructured, point cloud semantic segmentation has always been a challenging task. The graph-based method attempts to model the irregular point cloud by representing it as a graph; however, this approach incurs substantial computational cost due to the necessity of constructing a graph for every point within a large-scale point cloud. In this paper, we observe that boundary points possess more intricate spatial structural information and develop a novel graph attention network known as the Boundary-Aware Graph attention Network (BAGNet). On one hand, BAGNet contains a boundary-aware graph attention layer (BAGLayer), which employs edge vertex fusion and attention coefficients to capture features of boundary points, reducing the computation time. On the other hand, BAGNet employs a lightweight attention pooling layer to extract the global feature of the point cloud to maintain model accuracy. Extensive experiments on standard datasets demonstrate that BAGNet outperforms state-of-the-art methods in point cloud semantic segmentation with higher accuracy and less inference time.