Personalized recommendation aims at ranking a set of items according to the learnt preferences of the user. Existing methods optimize the ranking function by considering an item that the user has not bought yet as a negative item and assuming that the user prefers the positive item that he has bought to the negative item. The strategy is to exclude irrelevant items from the dataset to narrow down the set of potential positive items to improve ranking accuracy. It conflicts with the goal of recommendation from the seller's point of view, which aims to enlarge that set for each user. In this paper, we diminish this limitation by proposing a novel learning method called Hierarchical Visual-aware Minimax Ranking (H-VMMR), in which a new concept of predictive sampling is proposed to sample items in a close relationship with the positive items (e.g., substitutes, compliments). We set up the problem by maximizing the preference discrepancy between positive and negative items, as well as minimizing the gap between positive and predictive items based on visual features. We also build a hierarchical learning model based on co-purchase data to solve the data sparsity problem. Our method is able to enlarge the set of potential positive items as well as true negative items during ranking. The experimental results show that our H-VMMR outperforms the state-of-the-art learning methods.