The most important task in personalized news recommendation is accurate matching between candidate news and user interest. Most of existing news recommendation methods model candidate news from its textual content and user interest from their clicked news in an independent way. However, a news article may cover multiple aspects and entities, and a user usually has different kinds of interest. Independent modeling of candidate news and user interest may lead to inferior matching between news and users. In this paper, we propose a knowledge-aware interactive matching method for news recommendation. Our method interactively models candidate news and user interest to facilitate their accurate matching. We design a knowledge-aware news co-encoder to interactively learn representations for both clicked news and candidate news by capturing their relatedness in both semantic and entities with the help of knowledge graphs. We also design a user-news co-encoder to learn candidate news-aware user interest representation and user-aware candidate news representation for better interest matching. Experiments on two real-world datasets validate that our method can effectively improve the performance of news recommendation.