Abstract: Because of the high efficiency, compactness and avoiding sodium water reaction, the supercritical carbon dioxide (SCO₂) Brayton cycle is an ideal power conversion system for sodium-cooled fast reactors. In this paper, the 1 200 MWe Sodium-cooled Fast Reactor was used as the heat source of the system, and the temperature and heat load of the sodium loop were used as the operating boundary of the circulation system. The system performance and key equipment performance of different supercritical carbon dioxide Brayton cycles were compared. The coupling between the inter-stage cooling and recompression cycle and the characteristics of the heat source of the sodium-cooled reactor is the best, and the cycle efficiency is the highest (40.7%). Furthermore, the influence of different operating parameters on the efficiency of the inter-stage cooling and recompression cycle was studied, and the sensitivity of the efficiency of the circulation system to each of the key influencing factors was given. It is found that the efficiency of the circulation system is the most sensitive to the cold-end parameters, followed by the split ratio and turbine inlet parameters, and the weakest to the main compressor inter-stage pressure ratio.