Carbon Capture, Utilization, and Storage (CCUS) is an indispensable technique for reducing carbon dioxide emissions and enhancing gas recovery. Due to CO2 separation from the CO2-rich sulfur-containing waste gas being high cost, the co-injection technique of the CO2/H2S mixture is significant. Consequently, in this study, we studied the competitive adsorption behavior of CH4/CO2/H2S mixture adsorption in various pore sizes kerogen nanopores by Grand Canonical Monte Carlo (GCMC) and Equilibrium Molecular Dynamics (EMD) simulations (at 373.15 K and pressure up to 45 MPa). The adsorption density of the CH4/CO2/H2S mixture is greatly influenced by pore sizes. CO2 molecule tends to align parallel along kerogen surfaces, and the H atom of the H2S molecule tends to close to the kerogen surface only in 0.5 nm pore size. The excess adsorption, CE(i), the total interaction energy, and the specific interaction energy results show that the adsorption capacity of the kerogen surface is H2S > CO2 > CH4. The size of the average density of CO2, and H2S is 0.5 > 1 > 2 > 3 > 4 nm, but CH4 is the opposite. Overall, the effect of pore size for competitive adsorption leads to 0.5 nm to 1 nm pore size is better for CO2/H2S storage and shale gas exploitation. The findings from this study have important implications for CO2/H2S mixtures injection into kerogen reservoirs. It is the theoretical significance for the engineering of shale gas production and CO2/H2S storage.