Three new lanthanide metal-organic frameworks IRHs-(1-3) supported by cyamelurate linkers have been synthesized and structurally characterized. The incorporation of numerous heteroatoms (N and O) into the pore walls and the relatively small microchannels of these porous solids enhance bonding force of the host-guest interactions, thus promoting the adsorption of carbon dioxide (CO2) over methane (CH4). The nonpolar covalent bonds in methane also favor the less uptake due to the hydrophilic walls of these frameworks. Grand canonical Monte Carlo simulations were performed to determine the origin of the adsorption. The density isocontour surfaces show that CO2 is mainly adsorbed on the walls composed of organic linkers and around the metal sites, whereas no specific adsorption site is observed for CH4, which indicates weak interactions between the framework and the adsorbed gas. As expected, the simulations show that CH4 is not observed around the metal center due to the presence of H2O molecules. The excellent selectivity of CO2/CH4 binary mixture was predicted by the ideal adsorbed solution theory (IAST) via correlating pure component adsorption isotherms with the Toth model. At 25 °C and 1 bar, the CO2 and CH4 uptakes for IRH-3 were 2.7 and 0.07 mol/kg, respectively, and the IAST predicated selectivity for CO2/CH4 (1:1) reached 27, which is among the best value for MOF materials.