Molecular dynamics simulations were carried out to study the structural and transport properties of carbon dioxide, methane, and their mixture at 298.15 K in Na-montmorillonite clay in the presence of water. The simulations show that, the self-diffusion coefficients of pure CO 2 and CH 4 molecules in the interlayers of Na-montmorillonite decrease as their loading increases, possibly because of steric hindrance. The diffusion of CO 2 in the interlayers of Na-montmorillonite, at constant loading of CO 2 , is not significantly affected by CH 4 for the investigated CO 2 /CH 4 mixture compositions. We attribute this to the preferential adsorption of CO 2 over CH 4 in Na-montmorillonite. While the presence of adsorbed CO 2 molecules, at constant loading of CH 4 , very significantly reduces the self-diffusion coefficients of CH 4 , and relatively larger decrease in those diffusion coefficients are obtained at higher loadings. The preferential adsorption of CO 2 molecules to the clay surface screens those possible attractive surface sites for CH 4 . The competition between screening and steric effects leads to a very slight decrease in the diffusion coefficients of CH 4 molecules at low CO 2 loadings. The steric hindrance effect, however, becomes much more significant at higher CO 2 loadings and the diffusion coefficients of methane molecules significantly decrease. Our simulations also indicate that, similar effects of water on both carbon dioxide and methane, increase with increasing water concentration, at constant loadings of CO 2 and CH 4 in the interlayers of Na-montmorillonite. Our results could be useful, because of the significance of shale gas exploitation and carbon dioxide storage.