Three versions of zirconium-based metal organic frameworks, NH2-UiO-66, GMA-UiO-66, and EDA-UiO-66, were synthesized and employed as adsorbent for CO2/CH4 separation. GMA-UiO-66 was synthesized via a ring opening reaction between the amine species in the framework and epoxy groups in glycidyl methacrylate (GMA), while the green aza-Michael addition reaction was used for the first time to functionalize GMA-UiO-66 with ethylenediamine (EDA). The products were characterized by BET, XRD, TGA, FESEM, ICP-OES, H-1 NMR, mass spectroscopy, and FTIR-ATR methods to monitor their textural properties before and after functionalization. The results indicated that GMA was successfully grafted to the NH2-UiO-66 framework, and most of the alkene groups were grafted with EDA, which indicated that the Michael addition reaction was very effective. The experimental gas adsorption results indicated that the EDA-grafted UiO-66 possessed the highest CO2 adsorption capacity as well as CO2/CH4 selectivity due to the introduction of alkaline nitrogen groups on the surface, which could form strong quadrupole-dipole interactions as well as the chemical reaction with CO2. EDA-grafted UiO-66 exhibited a 53% increase in CO2 adsorption capacity and a 95% increase in CO2/CH4 adsorption selectivity at 298 K and 5 bar relative to the untreated NH2-UiO-66. Moreover, EDA-UiO-66 exhibited excellent stability in the cyclic CO2 adsorption-desorption runs, which indicated that no EDA leaching had occurred during this process.