We propose an unmanned aerial vehicle (UAV)ground base station (GBS) coordinated NOMA scheme where UAV and GBS are jointly serve the cell-edge users. To the best of our knowledge, this is the first work to investigate airground BSs coordination for UAV-assisted NOMA systems, by taking advantage of the interference between UAV and GBS. Therefore, the proposed UAV-GBS coordinated NOMA scheme achieves much higher sum rate of cell-edge users than the noncoordinated UAV-assisted NOMA schemes where interference is suppressed as much as possible. The proposed scheme also leads to better channel condition and more flexible and cost-effective interference management, compared to GBSs coordinated NOMA. We conduct joint optimization of power allocation, user scheduling and UAV trajectory for the UAV-GBS coordinated system. A closed-form optimal solution to power allocation is derived. In addition, a dedicated successive interference cancellation (SIC) ordering approach is proposed. It is proven that the selection of a cell-center user with higher SIC order contributes to a higher rate of cell-edge user, based on which an SIC order based user scheduling algorithm for both cell-center and cell-edge users is presented.