Social recommender systems have attracted a lot of attention from academia and industry. On social media, users' ratings and reviews can be observed by all users, and have implicit influence on their future ratings. When these users make subsequent decisions about an item, they may be affected by existing ratings on the item. Thus, implicit influence propagates among the users who rated the same items, and it has significant impact on users' ratings. However, implicit influence propagation and its effect on recommendation rarely have been studied. In this article, we propose an information propagation-based social recommendation method (SoInp) and model the implicit user influence from the perspective of information propagation. The implicit influence is inferred from ratings on the same items. We investigate the concrete effect of implicit user influence in the propagation process and introduce it into recommender systems. Furthermore, we incorporate the implicit user influence and explicit trust information in the matrix factorization framework. To demonstrate the performance, we conduct comprehensive experiments on real-world datasets to compare the proposed method with the state-of-the-art models. The results indicate that SoInp makes notable improvements in rating prediction.