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Face anti-spoofing (FAS) plays a vital role in securing face recognition systems. Existing methods heavily rely on the expert-designed networks, which may lead to a sub-optimal solution for FAS task. Here we propose the first FAS method based on neural architecture search (NAS), called NAS-FAS, to discover the well-suited task-aware networks. Unlike previous NAS works mainly focus on developing efficient search strategies in generic object classification, we pay more attention to study the search spaces for FAS task. The challenges of utilizing NAS for FAS are in two folds: the networks searched on 1) a specific acquisition condition might perform poorly in unseen conditions, and 2) particular spoofing attacks might generalize badly for unseen attacks. To overcome these two issues, we develop a novel search space consisting of central difference convolution and pooling operators. Moreover, an efficient static-dynamic representation is exploited for fully mining the FAS-aware spatio-temporal discrepancy. Besides, we propose Domain/Type-aware Meta-NAS, which leverages cross-domain/type knowledge for robust searching. Finally, in order to evaluate the NAS transferability for cross datasets and unknown attack types, we release a large-scale 3D mask dataset, namely CASIA-SURF 3DMask, for supporting the new 'cross-dataset cross-type' testing protocol. Experiments demonstrate that the proposed NAS-FAS achieves state-of-the-art performance on nine FAS benchmark datasets with four testing protocols.