The supercritical CO2 Brayton cycle is a potential technology in small modular reactors (SMRs), and the overall system efficiency can be significantly improved by optimizing the PCHE design parameters. This study develops a thermodynamic-economic analysis model for a supercritical CO2 simple Brayton cycle cooled SMR, with consideration of the detailed parameters of PCHEs. The impact of the length, channel number and channel type for the recuperator and the precooler on system thermal efficiency and levelized cost of electricity (LCOE) are analyzed. A dual-objective optimization study is conducted at the system level to identify the optimal design of size parameters and types for the heat exchangers. The results indicate that the influence of PCHE size parameters variations on system performance varies across different channel types. Additionally, the selection of the recommended recuperator type is influenced by the recuperator inlet Reynolds number. At the optimum design, the recommended channel type for recuperator and precooler are both S-shaped, resulting in a system efficiency of 39.12% and LCOE of 0.0456 $/kWe. The findings are valuable for enhancing energy utilization and reducing the power generation cost of SMRs.