Abstract: In this paper, we focus on nuclear norm regularized matrix completion model in large matrices, and propose a new model named stochastic sub-gradient method for low rank matrix completion (SS-LRMC). To the problem of traditional SVT algorithm that would use one fixed threshold to shrink all the singular values during iterations, and the enormous computation burden when faced with large matrices, we define an adaptive singular value thresholding operator, and put forward a kind of matrix completion model applicable for user-item rating matrix of collaborative filtering. During iterations, we combine stochastic sub-gradient descent techniques with the adaptive singular value thresholding operator to obtain low rank intermediate solutions. Empirical results confirm that our proposed model and algorithm outperform several state-of-the-art matrix completion algorithms and the application to collaborative filtering recommendation can effectively solve the sparse problem of the user-item rating matrix and can significantly improve recommendation accuracy.