Recommender systems have been successfully adopted as an effective tool to alleviate information overload and assist users to make decisions. Recently, it has been demonstrated that incorporating social relationships into recommender models can enhance recommendation performance. Despite its remarkable progress, a majority of social recommendation models have overlooked the item relations-a key factor that can also significantly influence recommendation performance. In this paper, a approach is first proposed to acquire item relations by measuring correlations among items. Then, a co-regularized recommendation model is put forward to integrate the item relations with social relationships by introducing co-regularization term in the matrix factorization model. Meanwhile, that the co-regularization term is a case of weighted atomic norm is illustrated. Finally, based on the proposed model a recommendation algorithm named CRMF is constructed. CRMF is compared with existing state-of-the-art recommendation algorithms based on the evaluations over four real-world data sets. The experimental results demonstrate that CRMF is able to not only effectively alleviate the user cold-start problem, but also help obtain more accurate rating predictions of various users.