In recent years, matrix factorization (MF) has been exploited commonly in recommender system because of its capability and simplification. However, data sparsity and cold-start problems make the latent feature of users learned by MF cannot represent the users' preferences and the similarity relation among users exactly, which limits the performance of MF. To remedy it, the regularized matrix factorization (RMF) draws researchers' attention. And the problem demanding prompt solution in RMF is capturing the reliable similarity relation among users. Besides, MF simply regards the inner product between the latent features of both target user and target item as the score that target user may rate the target item, ignoring the user's different attentions on various features of the item. How to analyze the user's attention on item's features and capture more accurate preference of the user is still a challenge. To address these issues, a model is put forward named attention-based regularized matrix factorization, abbreviated as ARMF. Specifically, to settle the problems of data sparsity and cold-start and obtain reliable similar relationships among users, the model builds a user-item heterogeneous network according to the social network and the rating record, and the similarities among users can be obtained based on it. Incorporating attention mechanism into MF allows us to analyze the attention of users on different item's features and capture moreaccurate preferences of users, which improves the precision of MF further. At last, the proposed model is compared with the state-of-the-art models on two real-world datasets and the result demonstrates the better precision and robustness of ARMF.