The CO2-enhanced coalbed methane recovery (CO2-ECBM) technique is based on competitive adsorption. In this study, three models of different coal ranks were established using the molecular dynamics (MD) method. A combination of MD and grand canonical Monte Carlo (GCMG) simulations was used to investigate the competitive adsorption of CO2/CH4 on dry and moist coal. The effects of coal rank and moisture content on pore structure, chemical structure, mixed gas adsorption capacity, and adsorption selectivity are discussed in detail. Simulation results show that from low- to high-rank coals, the total pore volume, porosity, and proportion of effective pores increase, which leads to an increase in their adsorption capacity. In addition, the oxygen-containing functional groups on the pore surface of coal enhance the displacement effect of CO2 on CH4 and with an increase in coal rank the adsorption selectivity of CO2/CH4 decreases. Moreover, the adsorption capacity of CO2 and CH4 will decrease owing to moisture. Water molecules will preferentially occupy the high-energy adsorption sites on the pore surface of coal, and then hydrogen bonding and capillary condensation will form water clusters. Therefore, in the case of moist coal, the adsorption selectivity of CO2 to CH4 fluctuates and shows different patterns of variation according to the different effective pore volumes of different coal ranks. From the perspective of CO2-ECBM, achieving a certain moisture content can have a beneficial effect, and the optimal moisture content of medium- and high-rank coal should be higher than that of low-rank coal. Under low-pressure conditions, the adsorption selectivity of CO2/CH4 of dry and moist coal is larger than that of high-pressure conditions. In our work, we advance the understanding of the microscopic mechanism of competitive adsorption of CO2/CH4, which provides a theoretical basis for improving CO2-ECBM technology.