Although Recommender Systems have been comprehensively studied in the past decade both in industry and academia, most of current recommender systems suffer from the following issues: 1) The data sparsity of the user-item matrix seriously affect the recommender system quality. As a result, most of traditional recommender system approaches are not able to deal with the users who have rated few items, which is known as cold start problem in recommender system. 2) Traditional recommender systems assume that users are independently and identically distributed and ignore the social relation between users. However, in real life scenario, due to the exponential growth of social networking service, such as facebook and Twitter, social connections between different users play an significant role for recommender system task. In this work, aiming at providing a better recommender systems by incorporating user social network information, we propose a matrix factorization framework with user social connection constraints. Experimental results on the real-life dataset shows that the proposed method performs significantly better than the state-of-the-art approaches in terms of MAE and RMSE, especially for the cold start users.