The system performance of the supercritical CO2 Brayton cycle for the Sodium Fast Reactor with a partial-cooling layout was studied, and an economic analysis was carried out. The energetic, exergetic, and exergoeconomic analyses are presented, and the optimized results were compared with the recompression cycle. The sensitivity analyses were conducted by considering the variations in the pressure ratios and inlet temperatures of the main compressor and the turbine. The exergy efficiency of the partial-cooling cycle reached 63.65% with a net power output of 34.39 MW via optimization. The partial-cooling cycle obtained a minimum total cost rate of 2230.36 USD/h and exergy efficiency of 63.65% when the pressure ratio was equal to 3.50. The inlet temperature of the main compressor was equal to 35 °C, and the inlet temperature of the turbine was equal to 480 °C. The total cost of recuperators decreased with the increase in the pressure ratio and the inlet temperatures of the main compressor. In addition, the total cost of recuperator could be reduced by increasing the outlet temperature of the turbine. The change in cost from exergy loss and destruction with the pressure ratio was substantially larger than with the inlet temperature of the turbine or the main compressor. Manipulating the pressure ratio is an essential method to guarantee good economy of the system. Moreover, capital investment, operation, and maintenance costs normally accounted for large proportions of the total cost rate, being almost double the cost from the exergy loss and destruction occurring in each condition.