Face presentation attacks have become an increasingly critical issue in the face recognition community. Many face anti-spoofing methods have been proposed, but they cannot generalize well on 'unseen' attacks. This work focuses on improving the generalization ability of face anti-spoofing methods from the perspective of the domain generalization. We propose to learn a generalized feature space via a novel multi-adversarial discriminative deep domain generalization framework. In this framework, a multi-adversarial deep domain generalization is performed under a dual-force triplet-mining constraint. This ensures that the learned feature space is discriminative and shared by multiple source domains, and thus is more generalized to new face presentation attacks. An auxiliary face depth supervision is incorporated to further enhance the generalization ability. Extensive experiments on four public datasets validate the effectiveness of the proposed method.