Aircraft electrification has become a tendency with demands for low carbon emissions and high electrical load capacity nowadays. Aircraft are especially strict with onboard weight; as a result, high-temperature superconducting (HTS) electrical machines are drawing attention for airborne applications due to their potential for a significant increase in power density. In this study, a feasible scheme of a hybrid-HTS airborne synchronous generator was proposed to fulfill the requirements of a small aircraft (with fewer than eight seats and a maximum range of about 1000 km). The full design from top to bottom is described. The output characteristics and metallic and superconducting AC losses were calculated based on the finite element method. The power grade of 1 MW was obtained, with a power density of 9.27 kW/kg and an efficiency of 98.73%. Furthermore, the performance of the machine was optimized using the Taguchi method. The preliminary design demonstrated the possibility and benefits of hybrid-HTS machines for airborne applications.