The near-far problem causes severe throughput unfairness in wireless powered communication networks (WPCN). In this paper, we exploit non-orthogonal multiple access (NOMA) technology and propose a fairness-aware NOMA-based scheduling scheme to mitigate the near-far effect and to enhance the max-min fairness. Specifically, we sort all users according to their channel conditions and divide them into two groups, the interference group with high channel gains and the noninterference group with low channel gains. The power station (PS) concurrently transmits energy signals with the data transmissions of the users in the interference group. Thus, the users in the noninterference group can harvest more energy and achieve a higher throughput, while the users in the interference group degrade their performance due to the interfering signals from the PS. We then apply order statistic theory to analyze the achievable rates of ordered users, based on which all users are appropriately grouped for NOMA transmission to achieve the max-min fairness of the system. Meanwhile, the optimal number of interfered users that determines the set of users in each group, is derived. Our simulation results validate the significant improvement of both network fairness and throughput via the fairness-aware NOMA-based scheduling scheme.