In recent years, domain adaptation techniques have been widely used to adapt face anti-spoofing models to a cross-scenario target domain. Most previous methods assume that the Presentation Attack Instruments (PAIs) in such cross-scenario target domains are the same as in the source domain. However, since malicious users are free to use any form of unknown PAIs to attack the system, this assumption does not always hold in practical applications of face anti-spoofing. Thus, unknown PAIs would inevitably lead to significant performance degradation, since samples of known and unknown PAIs usually have large differences. In this paper, we propose an Evidential Semantic Consistency Learning (ESCL) framework to address this problem. Specifically, a regularized evidential deep learning strategy with a two-way balance of class probability and uncertainty is leveraged to produce uncertainty scores for unknown PAI detection. Meanwhile, an entropy optimization-based semantic consistency learning strategy is also employed to encourage features of live and known PAIs to be gathered in the label-conditioned clusters across the source and target domains, while making the features of unknown PAIs to be self-clustered according to intrinsic semantic information. In addition, a new evaluation metric, KUHAR, is proposed to comprehensively evaluate the error rate of known classes and unknown PAIs. Extensive experimental results on six public datasets demonstrate the effectiveness of our method in generalizing face anti-spoofing models to both known classes and unknown PAIs with different types and quantities in a cross-scenario testing domain. Our method achieves state-of-the-art performance on eight different protocols.