Ethnic bias has proven to negatively affect the performance of face recognition systems, and it remains an open research problem in face anti-spoofing. In order to study the ethnic bias for face anti-spoofing, we introduce the largest up to date CASIA-SURF Cross-ethnicity Face Anti-spoofing (CeFA) dataset (briefly named CeFA), covering $3$ ethnicities, $3$ modalities, $1,607$ subjects, and 2D plus 3D attack types. Four protocols are introduced to measure the affect under varied evaluation conditions, such as cross-ethnicity, unknown spoofs or both of them. To the best of our knowledge, CeFA is the first dataset including explicit ethnic labels in current published/released datasets for face anti-spoofing. Then, we propose a novel multi-modal fusion method as a strong baseline to alleviate these bias, namely, the static-dynamic fusion mechanism applied in each modality (i.e., RGB, Depth and infrared image). Later, a partially shared fusion strategy is proposed to learn complementary information from multiple modalities. Extensive experiments demonstrate that the proposed method achieves state-of-the-art results on the CASIA-SURF, OULU-NPU, SiW and the CeFA dataset.