Traditional recommender systems are typically passive in that they try to adapt their recommendations to the user's historical interests. However, it is highly desirable for commercial applications, such as e-commerce, advertisement placement, and news portals, to be able to expand the users' interests so that they would accept items that they were not originally aware of or interested in to increase customer interactions. In this paper, we present Influential Recommender System (IRS), a new recommendation paradigm that aims to proactively lead a user to like a given objective item by progressively recommending to the user a sequence of carefully selected items (called an influence path). We propose the Influential Recommender Network (IRN), which is a Transformer-based sequential model to encode the items' sequential dependencies. Since different people react to external influences differently, we introduce the Personalized Impressionability Mask (PIM) to model how receptive a user is to external influence to generate the most effective influence path for the user. To evaluate IRN, we design several performance metrics to measure whether or not the influence path can smoothly expand the user interest to include the objective item while maintaining the user's satisfaction with the recommendation. Experimental results show that IRN significantly outperforms the baseline recommenders and demonstrates its capability of influencing users' interests.