To solve the problem that users and products can not be accurately selected in large data sets, and the problem that user behavior preference can not be predicted accurately, a new method of CUR (Column Union Row) matrix decomposition was proposed. A small number of columns were selected from the original matrix to form the matrix C, and a small number of rows were selected to form the matrix R. Then, the matrix U was constructed by Orthogonal Rotation (QR) matrix decomposition. The matrixes C and R were feature matrixes of users and products respectively, which were composed of real data, and enabled to reflect the detailed characters of both users as well as products. In order to predict behavioral preferences of users accurately, the authors improved the CUR algorithm in this paper, endowing it with greater stability and accuracy in terms of matrix recovery. Lastly, the experiment based on real dataset (Netflix dataset) indicates that, compared with traditional singular value decomposition, principal component analysis and other matrix decomposition methods, the CUR matrix decomposition algorithm has higher accuracy as well as better interpretability in terms of feature selection, as for matrix recovery, the CUR matrix decomposition also shows superior stability and accuracy, with a preciseness of over 90%. The CUR matrix decomposition has a great application value in the recommender system and traffic flow prediction.