Molecular dynamics simulation studies were employed to investigate the microscopic behaviors of CH4 and CO2 molecules in slit-nanopores (SNPs) with various surfaces and different compositions. Three kinds of SNPs were constructed by a pair-wise combination of graphene, silica, and the calcite surface. The grand canonical Monte Carlo and molecular dynamics simulation methods were used to investigate the adsorption and self-diffusion of the gases in the nanopores. It is found that in all three cases, the CH4 molecules prefer to adsorb onto the graphene surface, whereas the CO2 molecules prefer to adsorb onto the calcite surface. The adsorption intensity of gases adsorbed onto various surfaces, the adsorption distances, along with the details of adsorption orientations of CH4 and CO2 molecules on various surfaces are calculated. The surface characteristics, such as surface roughness and charge distribution, are analyzed to help understand the microscopic adsorption behaviors of the gases on the specific surface. It was found that competitive adsorptions of CO2 over CH4 broadly occurred, especially in the SNPs containing calcite, because of the strong adsorption interactions between the CO2 molecules and the calcite surface. This work provides the microbehaviors of CH4 and CO2 in SNPs with various surfaces in different compositions to provide useful guidance for better understanding about the microstate of gases in complex nanoporous shale formation and to give out useful guidance for enhancing shale gas recovery by injecting CO2.