MOF-based membranes, which have appropriate MOF dispersion and suitable interaction, have shown high CO2 permeability and significant CO2/CH4 and CO2/N2 selectivity. In this study, a layer of Pebax was coated on polysulfone (PSF), which this layer incorporated by various content of Cu-MOFs to improve the performance (permeability and CO2/CH4 and CO2/N2 selectivity) of all membranes. Characterization techniques such as SEM, TGA, BET, and gas adsorption verified that Cu-BTC was successfully dispersed into the Pebax matrix. Pure CO2 and CH4 gases permeation experiments were performed to investigate the impact of Cu-MOFs on the gas permeability of prepared MOF-based membranes. The “Pebax” embedded by 15 wt% CuBTC and 15 wt% of NH2-CuBTC over PSF support exhibited higher gas separation performance compared to the pristine one. They demonstrated a CO2 permeability of 228.6 and 258.3 Barrer, respectively, while the blank membrane had a CO2 permeability of 110.6 Barrer. Embedding the NH2-Cu-BTC intensified the interaction between incorporated MOF particles and the polymer phase that led to increase the CO2/CH4 and CO2/N2 selectivity. In addition, the performance of prepared membranes was evaluated at various feed pressures with the range of 2-10 bar. The CO2/CH4 and CO2/N2 separation was enhanced as the feed pressure surged.