The Non-negative Matrix Factorization （NMF） algorithm based on graph regularization makes full use of the assumption that high-dimensional data are usually located in a low-dimensional manifold space to construct the Laplacian matrix. The disadvantage of this algorithm is that the constructed Laplacian matrix is calculated in advance and will not be iterated during the multiplicative update process. In order to solve this problem， the self-representation method in subspace learning was combined to generate the representation coefficient， and the similarity matrix was further calculated to obtain the Laplacian matrix， and the Laplacian matrix was iterated during the update process. In addition， the label information of the training set was used to construct the class indicator matrix， and two different regularization items were introduced to reconstruct the category indicator matrix respectively. This algorithm was called Graph Learning Regularized Discriminative Non-negative Matrix Factorization （GLDNMF）， and the corresponding multiplicative update rules and the convergence proof of the objective function were given. Face recognition experimental results on two standard datasets show that the accuracy of the proposed algorithm for face recognition is increased by 1% - 5% compared to the existing classic algorithms， verifying the effectiveness of the proposed method.