In this paper, a novel system based on the combination of a supercritical recompression Brayton cycle (SRBC) and LiBr-H2O absorption refrigeration cycle (ARC) is proposed, in which ARC utilizes the waste heat of SRBC for cooling and further reduces the main compressor inlet temperature. The potential of using xenon and krypton as additives for the supercritical CO2 Brayton cycle is explored via comparative analysis. The results show that CO2/Krypton is more suitable to be the working fluid of the combined system because of its higher thermal efficiency and lower costs. The effects of the operating parameters and mass fraction of krypton on the thermo-economic performance of the combined system are discussed. Multi-objective optimization is applied to simultaneously optimize the thermal efficiency and total product unit cost of the system. Compared with the stand-alone cycle, the combined system can improve the cycle efficiency over a wide temperature range. The exergy efficiency of SRBC/ARC using CO2/Krypton (0.64/0.36) increased from 0.638 to 0.688, from 0.653 to 0.665, and from 0.586 to 0.646 at ambient temperature T0 = 10, 25, 35 °C, respectively, increasing by 7.84%, 1.84%, and 10.24% compared with that of SCO2RBC. The combined system will achieve its full potential when the critical temperature of the working fluid is close to the ambient temperature.