Benefiting from deep learning with large scale face databases, 2D face recognition has made significant progress in recent years. However, it still highly depends on lighting conditions and human poses, and suffers from face spoofing problem. In contrast, 3D face recognition reveals a new path that can overcome the previous limitations of 2D face recognition. One of the most important problems for 3D face recognition is to construct a suitable database, which can be exploited to train different 3D face recognition algorithms. In this work, we propose a new database, CAS-AIR-3D Face, for low-quality 3D face recognition. It includes 24713 videos from 3093 individuals, which is captured by Intel RealSense SR305. The database contains three modalities: color, depth and near infrared, and is rich in pose, expression, occlusion and distance variations. To the best of our konwledge, CAS-AIR-3D Face is the largest low-quality 3D face database in terms of the number of individuals and the sample variations. Moreover, we preprocess the data via a sophisticated face alignment method, and Point Cloud Spherical Cropping Method (SCM) is leveraged to remove the background noise in the depth images. Finally, an evaluation protocol is designed for fair comparison, and extensive experiments are conducted with different backbone networks to provide different baselines on this database.