In this study, grand canonical Monte Carlo simulation was carried out to systematically study the effects of extra-framework cations on the capacity of storage and separation of carbon dioxide (CO2) and methane (CH4) in cation-exchanged rho-zeolite-like metal-organic framework (rho-ZMOF). Monovalent (Na+, NH4 + and Li+), divalent (Mg2+ and Sr2+) and trivalent (Al3+) cations with different ion radii were adopted as the representative extra-framework cations. The simulations of the single-component adsorption of CO2 molecules indicate that the varieties in extra-framework cations do not bring evident differences in the dispersion interaction contributions to the isosteric adsorption heats of CO2 but rather the electrostatic interaction contributions. Higher the valence a cation has, stronger the electrostatic interaction with CO2 is and, therefore, a higher storage capacity, though the corresponding accommodation number of the extra-framework cations is smaller. For the cations having the same valence, the storage capacity decreases with the increase in the accessible surface area and total free volume of the host structure. The single-component adsorption isotherms of CO2 and CH4 can be described by a dual-site Langmuir–Freundlich equation. Under typical operating conditions (298 K and 1 atm) in a pressure swing adsorption (PSA) process, the simulation results of the adsorption of CO2 and CH4 mixture demonstrate that the Al-exchanged rho-ZMOF exhibits an unprecedented high selectivity of CO2 over CH4 up to 112, compared with other metal-organic frameworks and nanoporous materials reported to date. Our results suggest that the variation of extra-framework cations is an efficient way to improve the adsorption capacity of the rho-ZMOF for the storage and separation of CO2 and CH4 mixtures using the PSA process at ambient temperature and pressure.