In this paper, an unmanned aerial vehicle (UAV)-enabledspace-air-ground integrated relay system, in which UAV is equipped with phased-array antennas to receive satellite’s signal while utilizing non-orthogonal multiple access (NOMA) schemes to transmit data to land-based users, is proposed. For UAV signal collection, a detection-vector optimization problem can be addressed by introducing a serial of transformations into a second-order cone programming problem. Furthermore, the UAV-ground NOMA communication is summarized into a max-min problem in terms of UAV’s energy efficiency (EE), which is a fractional mixed-integer non-convex problem and has been widely recognized as hard work. Thus, a two-step solution is proposed. Firstly, we transfer the max-min fractional problem into a subtractive one. After that, the transformed problem is further divided into three sub-problems, which are used for jointly performing UAV trajectory optimization, NOMA scheduling optimization, and NOMA power allocation. In addition, the non-convexity of the above-mentioned problem is well solved by using the proposed iterative algorithm, achieving a rapid convergence. Numerical results illustrate the superiority of the proposed EE-NOMA scheme, which achieves three times higher energy-efficient than the conventional spectrum efficiency scheme, and NOMA is shown to globally outperform the orthogonal multiple access in UAV EE circumstance.