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Supercritical carbon dioxide (S-CO₂) Brayton cycle technology has the advantages of excellent energy density and heat transfer. The compressor is the most critical and complex component of the cycle. Especially, in order to make the system more reliable and economical, the design method of a high efficiency compressor without a high speed requirement is particularly important. In this paper, thermodynamic design software of a S-CO₂ centrifugal compressor is developed. It is used to design the 150 kW grade S-CO₂ compressor at the speed of 40,000 rpm. The performance of the initial design is carried out by a 3-D aerodynamic analysis. The aerodynamic optimization includes three aspects: numerical calculation, design software and the flow part geometry parameters. The aerodynamic performance and the off-design performance of the optimal design are obtained. The results show that the total static efficiency of the compressor is 79.54%. The total pressure ratio is up to 1.9. The performance is excellent, and it can operate normally within the mass flow rate range of 5.97 kg/s to 11.05 kg/s. This research provides an intelligent and efficient design method for S-CO₂ centrifugal compressors with a low flow rate and low speed, but high pressure ratio.