Abstract: In order to solve the problem of low resolution of face image, this paper proposes a algorithm for low resolution face image recognition which utlize the coupled nonnegative matrix factorization and maintains the coefficient relaxation (RCNMF). First, the nonnegative matrix factorization (NMF) is performed for high-resolution and low-resolution face images. Secondly, the combination coefficients are kept approximately the same while decomposing, so as to obtain the base matrices of high-resolution and low-resolution images. Finally, the features of training and test samples are extracted by the basis matrix of low resolution images for recognition. Our experiments verify that the RCNMF algorithm is more effective to solve low resolution face recognition problem than the other state-of-the-art methods based on coupled mapping. At the same time, the convergence of the proposed RCNMF algorithm is verified by experiments.