3D mask spoofing attack has been one of the main challenges in face recognition. A real face displays a different motion behaviour compared to a 3D mask spoof attempt, which is reflected by different facial dynamic textures. However, the different dynamic information usually exists in the subtle texture level, which cannot be fully differentiated by traditional hand-crafted texture-based methods. In this paper, we propose a novel method for 3D mask face anti-spoofing, namely deep convolutional dynamic texture learning, which learns robust dynamic texture information from fine-grained deep convolutional features. Moreover, channel-discriminability constraint is adaptively incorporated to weight the discriminability of feature channels in the learning process. Experiments on both public datasets validate that the proposed method achieves promising results under intra and cross dataset scenario.