Group recommendation has attracted significant research efforts for its importance in benefiting a group of users. This paper investigates the Group Recommendation problem from a novel aspect, which tries to maximize the satisfaction of each group member while minimizing the unfairness between them. In this work, we present several semantics of the individual utility and propose two concepts of social welfare and fairness for modeling the overall utilities and the balance between group members. We formulate the problem as a multiple objective optimization problem and show that it is NP-Hard in different semantics. Given the multiple-objective nature of fairness-aware group recommendation problem, we provide an optimization framework for fairness-aware group recommendation from the perspective of Pareto Efficiency. We conduct extensive experiments on real-world datasets and evaluate our algorithm in terms of standard accuracy metrics. The results indicate that our algorithm achieves superior performances and considering fairness in group recommendation can enhance the recommendation accuracy.