In this work, we consider a downlink millimeter-wave (mmWave) communication scenario where a UAV base station (UAV-BS) equipped with a large-scale antenna array serves several ground users via hybrid beamforming. In order to save the power consumption of aerial UAV-BS, we consider the hybrid beamforming structure with fewer RF chains, and design the multi-user hybrid beamforming algorithm with the goal of minimizing the total transmit power. In order to ensure the quality of service (QoS) of ground users, the fairness transmission rate is considered. Furthermore, we take the resolution of analog phase shifter (PS) into account, and the beamforming problem turns into a mixed-integer nonlinear programming (MINLP). We also propose an improved Riemann gradient descent algorithm to solve the MINLP. Numerical results on the transmission power, beam pattern, and energy efficiency of the proposed algorithms are presented, showing that it allows hybrid systems to approach the performance of optimal fully-digital systems even PS resolution is constrained.