Abstract Standard convolution is inherently limited for semantic segmentation of point cloud due to its isotropy about features. It neglects the structure of an object, results in poor object delineation and small spurious regions in the segmentation result. This paper proposes a novel graph attention convolution (GAC), whose kernels can be dynamically carved into specific shapes to adapt to the structure of an object. Specifically, by assigning proper attentional weights to different neighboring points, GAC is designed to selectively focus on the most relevant part of them according to their dynamically learned features. The shape of the convolution kernel is then determined by the learned distribution of the attentional weights. Though simple, GAC can capture the structured features of point clouds for finegrained segmentation and avoid feature contamination between objects. Theoretically, we provided a thorough analysis on the expressive capabilities of GAC to show how it can learn about the features of point clouds. Empirically, we evaluated the proposed GAC on challenging indoor and outdoor datasets and achieved the state-of-the-art results in both scenarios.