Supercritical carbon dioxide (S-CO2) Brayton cycle has caught the attention in many fields, especially the field of nuclear reactors. The recompression cycle is considered to be one of the most feasible cycles to solve the pinch problem of heat exchanger. Aiming at the disadvantages of conventional cycle analysis, this paper proposed sensitivity analysis of several parameters and global parameter optimization. The result of sensitivity analysis showed that maximum pressure and efficiency of turbine had the most influential power upon relevant parameters that may determine the final cycle efficiency, followed by re-compressor efficiency, split ratio and main compressor efficiency, with total pressure loss the least. Based on the sensitivity analysis, the thermodynamic parameters optimizing with cycle efficiency as its objective function was presented in this paper. The global parameter optimization results indicated that, for the recompression cycle, the optimal pressure and split ratio could maximize the cycle efficiency. The cycle efficiency could be maximized to 0.447 by adjusting the split ratio and the maximum pressure to 0.687 and 27.75 MPa, while the heat source temperature was 600 degrees C, the efficiency of the compressor and re-compressor was 0.8 and the efficiency of turbine was 0.9. Depending on the simulation dates of optimization, criterion formulas of cycle efficiency, maximum pressure and split ratio under the best operating conditions were established. With the input values of given system parameters, the key cycle parameters under the best operating conditions could be received easily and accurately by the criterion formulas.