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The electric aircraft propulsion system requires high speed and high power-weight ratio electrical machines. This paper presents a superconducting homopolar inductor machine (HIM) based on HTS REBCO magnets, which could be a promising candidate for high power density electrical machines for future electric aircraft propulsion system. The HTS-HIM has a simple structure, high rotating speed, and huge potential to achieve a high power-weight ratio (kW/kg). This paper presents our design of a 10 kW HTS-HIM with a rotating speed of 3000 rpm. The structure and crucial parameters of HTS-HIM are presented. A 2D-axial pancake coil model for HTS REBCO magnets was built by using COMSOL. Based on this model, HTS REBCO magnets were design and optimized. The loss of REBCO magnets was also calculated. Finally, the output performance of the 10 kW HTS-HIM was simulated. Our work provides preliminary simulation and analysis for future MW-class HTS-HIM.