Geological CO2 sequestration (GCS) in depleted shale reservoirs is recognized as one of promising techniques to mitigate CO2 emissions, while the high cost of CO2 purification greatly hinders its deployment. Co-injection of CO2/H2S mixtures has been proposed as an economical alternative to further promote GCS application. In this work, we used Grand Canonical Monte Carlo (GCMC) and molecular dynamic (MD) simulations to investigate CO2/H2S mixture adsorption in organic and inorganic shale nanopores (at 333.15 K and pressure up to 50 MPa). CO2 and H2S present distinct adsorption behaviors on the different surfaces. H2S adopts unordered structures on kerogen surfaces, but a perpendicular orientation on illite due to H-bonding, which also results in higher adsorption, while CO2 is preferentially distributed parallel along the surfaces. Furthermore, CO2 and H2S accumulate in the concave parts of kerogen surfaces, while they concentrate around the tetrahedral aluminum (AT) atoms and K+ cations on illite surfaces. The adsorption selectivity of H2S over CO2 is always greater than 1, indicating the stronger adsorption propensity of H2S. The preferential adsorption of H2S on illite surface is facilitated by the stronger dipole–dipole interactions. PMF results show that the binding interaction between CO2 or H2S and illite is higher than on kerogen, and H2S always shows a stronger interaction than CO2. Overall, the total CO2 and H2S adsorption is higher in illite nanopores, implying a new promising storage method. This study provides important insights into the competitive adsorption mechanisms of CO2 and H2S in depleted shale reservoirs and sheds light on how sour gas geological sequestration capacity can be further improved.