Abstract: Dictionary learning is one of the most important feature representation methods. It has a wide range of applications in face recognition and other aspects. It is particularly suitable for solving face recognition problems under the change of pose, and has attracted much attention from many researchers. In order to enhance the discriminative ability of dictionary, researchers have put forward a large number of dictionary learning models in combination with domain knowledge and anti-noise strategies, including the recently proposed methods for simultaneous dimensionality reduction and dictionary learning, but these methods focus on the specific-class samples and fail to consider the sharing information between training samples. Therefore, we propose a fast low-rank shared dictionary learning with sparsity constraints approach. The method learns dimensionality reduction and dictionary jointly, and embeds Fisher discriminant criteria to obtain specific-class dictionary and coding coefficients. At the same time, we enforce a low-rank constraint to obtain the low-rank shared dictionary to enhance the discriminative ability of dictionary and coding coefficients. In addition, the Cayley transform is used to protect the orthogonality of the projection matrix to catch a compact feature set. Face recognition experiments on AR, Extended Yale B, CMU PIE, and FERET datasets demonstrate the superiority of our approach. The experimental results show that the proposed method has strong robustness to face recognition under facial expression changes, and plays an inhibitory role in lighting. It is especially suitable for solving small sample problems under illumination and expression changes.