Owing to the well-developed nano-porosity, the Shale reservoir could offer substantial storage capacity and become a potential candidate for CO2 geological sequestration gradually. However, the industry waste gas typically contains H2S impurities in addition to CO2 components, and the purification of such waste gas consumes large economic costs. Hence, the co-sequestration of CO2/H2S emerges as a viable alternative. Yet, the micro-mechanisms of CO2/H2S co-sequestration and CH4 displacement in shale reservoirs remain unclear. This study employs Grand Canonical Monte Carlo (GCMC) simulations to investigate the competitive adsorption of CO2/CH4 in shale illite nanopores of various mole fractions (i.e. 2:8, 6.5:3.5 and 5:5) and CH4:H2S:CO2 = 5:1:4. Considering the high temperature and pressure condition of shale formation, the temperature during the GCMC simulation is set as 373.15K, and the pressures reach up to 40MPa. Results reveal that the excess adsorption of CO2 and CH4 exhibits an increasing-then-decreasing trend with pressure, with CH4's excess adsorption diminishing beyond 20MPa. Absolute adsorption conforms closely to the Langmuir model. The competitive adsorption selectivity coefficient of CO2/CH4 diminishes with increasing CO2 mole fraction, suggesting its superior ability to displace CH4 under low mole fraction conditions. In the three-component adsorption, H2S demonstrates strong competitive adsorption, exceeding both CO2 and CH4 in adsorption density, resulting in reduced CH4 molecular numbers in both the adsorbed phase and pores, consequently diminishing the adsorption of CH4 and CO2 correspondingly. These findings elucidate the competitive adsorption behaviors of CO2/CH4 and CH4/H2S/CO2 in illite nanopores, providing a theoretical basis for CO2/H2S co-sequestration and enhanced recovery.