Cold start and data sparsity greatly affect the recommendation quality of collaborative filtering. To solve these problems, social recommendation algorithms introduce the corresponding user trust information in social network, however, these algorithms typically utilize only adjacent trusted user information while ignoring the social network connectivity and the differences in the trust influence between indirect users, which leads to poor accuracy. For this deficiency, this paper proposes a social recommendation algorithm based on user influence strength. First of all, we get the user influence strength vector by iterative calculation on social network and then achieve a relatively complete user latent factor according to near-impact trusted user behavior. Depending on such a user influence vector, we integrate user-item rating matrix and the trust influence information. Experimental results show that it has a better prediction accuracy, compared to the state-of-art society recommendation algorithms.