Abstract: A privacy-preserving collaborative filtering algorithm based on non-negative matrix factorization(NMF) is presented.The randomized perturbation techniques are used in the course of user data collection,and the collected data are processed by NMF,therefore,the users' privacy can be protected.The algorithm produces the recommendation based on the data of the privacy-preserving users.Theoretical analysis and experiment results show that the algorithm can not only protect the users' privacy,but also generate recommendations with decent accuracy.