•The preferential adsorption of CO2 over CH4 improves with coal rank.•Pore structure of coal affects the thermodynamics of adsorption of CO2 and CH4.•Adsorbed CO2 has a more ordered configuration than CH4 on different rank coals. In this paper, the pore structures of three different rank coals sampled from China (anthracite, bituminous coal and lignite) were characterized by CO2 and N2 adsorption. The isothermal adsorption curves of CO2 and CH4 on three samples were measured by gravimetric method and fitted by Langmuir model. The preferential selectivity (αCO2/CH4) was calculated using the Langmuir parameters of CO2 and CH4, and the Henry’s coefficient (KH) was obtained with the help of virial equation. More importantly, a comparative analysis of adsorption thermodynamics of CO2 and CH4 on three different rank coals, including surface potential (Ω), Gibbs free energy change (ΔG) and entropy loss (ΔS), was presented according to the adsorption data. It is found that the uptakes of CO2 and CH4 on anthracite are the largest, followed by lignite and bituminous coal in sequence. αCO2/CH4 increases with the increase of coal rank. Low temperature helps injected CO2 to displace pre-adsorbed CH4. The KH values on anthracite are the biggest, while KH values on bituminous coal are the smallest. Ω, ΔG and ΔS of CO2 and CH4 all exhibit a U-shaped function with maturity. Anthracite has the highest Ω, ΔG and ΔS, while bituminous coal has the lowest Ω, ΔG and ΔS. The thermodynamics parameters of Ω, ΔG and ΔS are affected by pore size distributions of three coals. Ω, ΔG and ΔS of CH4 are smaller than those of CO2. CO2 adsorption on coal is more favorable and spontaneous, and adsorbed CO2 molecules form a more efficient packing on coal.