In 2007, we developed a prototype refrigerator with a small turbo-expander to provide adequate cooling power (2 kW at 70 K) for HTS (High Temperature Superconductor) power machines. The reverse-Brayton cycle with neon gas as a working fluid was adopted in the refrigerator. The prototype refrigerator does not have enough COP (Coefficient of Performance) for practical HTS applications, and the purpose of this study is to research the information required for designing a new neon refrigerator with improved performance. We take the same refrigeration cycle and working fluid as the prototype one adopted, but a lower process pressure of 1 MPa/0.5 MPa is chosen instead of 2 MPa/1 MPa. The lower process pressure is required by the turbo-compressor design and the refrigeration process is analyzed by using a newly developed process simulator. Also, a heat-exchanger configuration is studied to make the refrigerator size small. The new refrigerator will have a cooling power of 2.5 kW at 65 K, and a COP of 0.06 at 80 K.