It is significant to understand the adsorption mechanisms of shale gas (CH4) and CO2 in shale formations to enhance CH4 recovery rates and enable geological CO2 storage. This study provides a comprehensive investigation into the adsorption behaviors of CO2 and CH4 within dry and hydrous calcite nanopores, utilizing a combination of grand canonical Monte Carlo simulations, molecular dynamics simulations, and density functional theory calculations. In dry calcite slits, the calculated results for the adsorption capacity, density profile, and isosteric heat of CO2 and CH4 reveal that CO2 possesses a stronger adsorption affinity, making it preferentially adsorb on the pore surface compared to CH4. In hydrous calcite slits, calculating the adsorption capacity and density profile of CO2 and CH4, the results show that the gas adsorption sites become progressively occupied by H2O molecules, leading to a substantial decrease in the adsorption capacity of CO2 and CH4. Furthermore, by analysis of the adsorption energy and electronic structure, the reason for the reduction of gas adsorption capacity caused by H2O is further revealed. This work has a deep understanding of the adsorption mechanisms of shale gas and CO2 in calcite and can offer valuable theoretical insights for the development of a CO2-enhanced shale gas recovery technology.