Abstract The traditional recommendation systems usually aim to improve the recommendation accuracy while overlooking the diversity within the recommended lists. Although some diversification techniques have been designed to recommend top-k items in terms of both relevance and diversity, the coverage of the user’s interest is overlooked. In this paper, we propose a general framework to recommend relevant and diverse items which explicitly takes the coverage of user interest into account. Based on the theoretical analysis, we design efficient greedy algorithms to get the near optimal solutions for those NP-hard problems. Experimental results on MovieLens dataset demonstrate that our approach outperforms state-of-the-art techniques in terms of both precision and diversity.