News recommender systems are essential for helping users to efficiently and effectively find out those interesting news from a large amount of news. Most of existing news recommender systems usually learn topic-level representations of users and news for recommendation, and neglect to learn more informative aspect-level features of users and news for more accurate recommendation. As a result, they achieve limited recommendation performance. Aiming at addressing this deficiency, we propose a novel Aspect-driven News Recommender System (ANRS) built on aspect-level user preference and news representation learning. Here, \textit{news aspect} is fine-grained semantic information expressed by a set of related words, which indicates specific aspects described by the news. In ANRS, \textit{news aspect-level encoder} and \textit{user aspect-level encoder} are devised to learn the fine-grained aspect-level representations of user's preferences and news characteristics respectively, which are fed into \textit{click predictor} to judge the probability of the user clicking the candidate news. Extensive experiments are done on the commonly used real-world dataset MIND, which demonstrate the superiority of our method compared with representative and state-of-the-art methods.