Unmined and undisturbed coal seams are considered favorable areas for CO2 storage. Studying the adsorption behavior of CO2/CH4 in carbon structures is critical to provide information for CO2 sequestration and gas exploitation. Here, three carbon structure models with different fringe lattices (curvature, planar, and a mixture lattice with curvature and planar) were constructed using an amorphous cell module in Material studio. The simulated densities of the curvature, planar, and mixture models were 1.4, which is within the range of the experimental density of coal. The adsorption behaviors of CH4, CO2, and their mixtures in the constructed models were investigated using the grand canonical Monte Carlo method. The results show that the absolute adsorption amount increases with the increasing ambient pressure and decreases with the increasing ambient temperature. The isosteric heat for adsorption of CO2 in three models is higher than that of CH4. The absolute adsorption amount of CO2/CH4 in the curvature model is higher than that in the other models, but the absolute adsorption amount of CO2 molecules is superior to that of CH4 at the same pressure and temperature. The adsorption sites for CO2/CH4 are concentrated in the pore space in the saturated adsorption state, and the saturated adsorption amount in the three models follows the sequence of curvature > mixture > planar. The pore width in the planar model shows a peak at 3-3.5 angstrom, whereas that in the mixture structure shows two peaks at 2.6-3.4 and 3.5-4.4 angstrom. However, the curvature model has wide intervals at 2.6-3.4 and 3.4-4.6 angstrom. The radial distribution function indicates that CH4/CO2 prefers to be adsorbed on C4 (sp(3), generic 4 bonds) and C3a (sp(2), double bond to C, C=C) and preferentially occupies the sites of curvature.