The high temperature superconductivity(HTS) cable must be cooled below the nitrogen liquefaction temperature to applicate the cable in power generation and transmi-ssion system under the superconducting state. To obtain superconducting state. a reliable cryocooler system is required. Structural and thermal design have been performed to design cryocooler system operated with reverse Brayton cycle using gas neon as refrigerant. This cryocooler system consists of compressor. recuperator. coldbox. control valves and has 1 kW cooling capacity. Heat loss calculation was conducted for the given cryocooler system by considering the conduction and radiation through the multi-layer insulation(MLI) and high vacuum. The results can be summarized as: conduction heat loss is 7 W in valves and access port and radiation heat loss is 18 W through the surface of cryocooler. The full design specifications were discussed and the results were applied to construct in house HTS cable cooling system.