Face anti-spoofing plays a crucial role in protecting face recognition systems from various attacks. Previous model-based and deep learning approaches achieve satisfactory performance for 2D face spoofs, but remain limited for more advanced 3D attacks such as vivid masks. In this paper, we address 3D face anti-spoofing via the proposed Hypergraph Convolutional Neural Networks (HGCNN). Firstly, we construct a computation-efficient and posture-invariant face representation with only a few key points on hypergraphs. The hypergraph representation is then fed into the designed HGCNN with hypergraph convolution for feature extraction, while the depth auxiliary is also exploited for 3D mask anti-spoofing. Further, we build a 3D face attack database with color, depth and infrared light information to overcome the deficiency of 3D face anti-spoofing data. Experiments show that our method achieves the state-of-the-art performance over widely used 3D and 2D databases as well as the proposed one under various tests.