Abstract: Considering that data used in many applications are intrinsically in matrix form rather than in vector form, this paper focuses on the generalized version of the problem of a low-rank approximation of a matrix with missing components, i.e. low-rank approximations of a set of matrices with missing components. This generalized problem is formulated as an optimization problem at first, which minimizes the total reconstruction error of the known components in these matrices. Then, an iterative algorithm is designed for calculating the generalized low-rank approximations of matrices with missing components, called GLRAMMC. Finally, detailed algorithmic analysis is given. Extensive experimental results on synthetic data as well as on real image data show the effectiveness of our proposed algorithm.