Sparse representation-based classification (SRC) method has achieved good recognition results and shown strong robustness for face recognition, especially when the face image is affected by illumination variations, expression changes and occlusion. SRC method simply uses the training set as a dictionary to encode test samples. However, the high-dimensional training face data usually contain a large amount of redundant information, which will increase the complexity of this method. Therefore, the image dimensionality reduction procedure is separately performed by most of the existing methods before SRC is launched, but this may not be able to make full use of the discriminative information of the training samples. In this paper, based on the efficient SRC method, a sparse embedding dimensionality reduction strategy is combined with to achieve a face recognition method. For the proposed method, a projection matrix is used to project high-dimensional data into a low-dimensional space. At the same time, a discriminative coefficient constraint term in the objective function is introduced to reduce the classification residual of the sample through the distance relationship between all coefficients. Then the label information of the sample is used to iteratively update the projection matrix and coefficient representation. Finally, the test samples are projected into the low-dimensional space for classification. A large number of experimental results on three widely used face datasets show that the proposed method improves the discrimination of face images in low-dimensional space and can achieve better face recognition results.