•We have proposed a graph attentional convolution network for 3D dental model segmentation.•We have proposed a local spatial augmentation module that can adaptively capture the local structure of dental model.•We have designed a learning-based graph attention mechanism to learn local geometric features from dental model.•We achieved best segmentation performance on a real-patient dataset when compared with state-of-the-art methods for 3D shape segmentation. Precisely segmenting teeth from digitized 3D dental models is an essential task in computer-aided orthodontic surgical planning. In recent years, various deep learning-based methods have been proposed to process dental models for teeth segmentation, however, these methods usually ignore or coarsely model the dependency between vertices/mesh cells in local space, which fails to exploit local geometric details that are critical to capture complete teeth structure. In this paper, we propose a specific end-to-end network for teeth segmentation on 3D dental models. By constructing a graph for the raw mesh data, our network adopts a series of graph attentional convolution layers and a global structure branch to extract fine-grained local geometric feature and global feature, respectively. Subsequently, these two features are further fused to learn comprehensive information for cell-wise segmentation tasks. We have evaluated our network on a real-patient dataset of dental models acquired through 3D intraoral scanners, and experimental results show that our method outperforms state-of-the-art deep learning methods for 3D shape segmentation.