Abstract: The purpose of this study is to design a compact and efficient cycle system. A suitable recompression S-CO₂ Brayton cycle is designed by combining with a nuclear power system with a medium core outlet temperature. The optimal design of the recompression Brayton cycle for the nuclear energy system with medium core outlet temperature under water cooled and dry cooled conditions are carried out with consideration of the recuperator temperature difference constraints and the cycle efficiency. The effects of the compressor inlet pressure and temperature, turbine inlet pressure, recuperator UA, turbomachinery efficiency and other parameters on the recompression Brayton cycle efficiency are studied in this paper. Under water-cooled conditions, the optimal cycle efficiency of the recompression Brayton cycle can reach 40.48%. Under dry-cooled conditions, the optimal cycle efficiency of the recompression Brayton cycle can reach 34.36%（compressor inlet temperature is 55 ℃）. Every time the compressor inlet temperature increases by 5%, the cycle efficiency of the recompression Brayton cycle decreases by 1.2%.