In this paper, we focus on recommending an item set to multiple users. Group recommender systems are designed to deal with the issue of recommending items for a user group. However, in some scenarios where different items are packed together as a gift set, such as gift set promotion, album promotion, we need to focus on consumers' preferences to multiple items rather than to some specific item. To deal with this issue, we pioneer a Nash equilibrium based Item Group Recommendation approach (NIGR). Specifically, we evaluate each consumer's preference to an item group from two perspectives, attraction part from the customer herself and social affection from her friends. Then, we model the recommending process as a game to achieve Nash equilibrium. Finally, we demonstrate the effectiveness of our approach with extensive experiments.