Matrix approximation (MA) methods are integral parts of today's recommender systems. In standard MA methods, only one feature vector is learned for each user/item, which may not be accurate enough to characterize the diverse interests of users/items. For instance, users could have different opinions on a given item, so that they may need different feature vectors for the item to represent their unique interests. To this end, this article proposes a mixture matrix approximation (MMA) method, in which we assume that the user-item ratings follow mixture distributions and the user/item feature vectors vary among different stars to better characterize the diverse interests of users/items. Furthermore, we show that the proposed method can tackle both rating prediction and the top-N recommendation problems. Empirical studies on MovieLens, Netflix and Amazon datasets demonstrate that the proposed method can outperform state-of-the-art MA-based collaborative filtering methods in both rating prediction and top-N recommendation tasks.