Abstract: The matrix factorization is one of the most powerful tools in collaborative filtering recommender systems. The Bayesian Probabilistic Matrix Factorization (BPMF) model has advantages of high prediction accuracy, but can not capture non-linear relationships between latent factors. To address this problem, an improved model is proposed based on the Logistic function and Markov Chain Monte Carlo is used to train the proposed model. Experiments on two real-world benchmark datasets show significant improvements in prediction accuracy compared with several state-of-the-art methods for recommendation tasks.