Abstract Collaborative filtering with large amount of user data will raise serious risk privacy of individuals. How to protect private data information from disclosure has become one of the greatest challenges to recommender systems. Differential privacy has emerged as a new paradigm for privacy protection with strong privacy guarantees against adversaries with arbitrary background knowledge. Although several studies explored privacy-enhanced neighborhood-based recommendations, little attention has been paid to privacy preserving latent factor models. To address the problem of privacy preserving in recommendation systems, a new collaborative filtering recommendation algorithm based on differential privacy is proposed in this paper, which achieves trade-off between recommendation accuracy and privacy by matrix factorization technique. Firstly, user and item latent feature matrices are constructed for decreasing sparsity. After that, matrix factorization model with noise is generated by adding the differential noisy using objective perturbation method, and then stochastic gradient descent is utilized to minimize regularized squared error function and learn the parameters of model. Finally, we apply a differentially private matrix factorization model to predict the ratings and conduct experiments on the MovieLens and Netflix datasets to evaluate its effectiveness. The experimental results demonstrate that our proposal is efficient and has limited side effects on the precision of recommendation.