Combination of the polyimide 6FDA-mPD (6FDA = 4,4'-hexafluoroisopropylidene diphthalic anhydride and mPD = m-phenylenediamine) and crystallites of the metal-organic frameworks (MOFs) MIL-101(Cr) or MOF-199 (HKUST-1, Cu-BTC) produces mixed-matrix membranes (MMMs) with excellent dispersion and compatibility of the MOF particles within the polymer matrix. Permeation tests of a binary CO2/CH4 (50/50) gas mixture showed a remarkable increase of CO2 permeabilities for MIL-101(Cr)@6FDA-mPD and significantly higher selectivities for MOF-199@6FDA-mPD. The CO2 permeability increased from 10 (neat polymer) to 50 Barrer for the 24 wt% MIL-101(Cr)@6FDA-mPD membrane (with essentially constant selectivity) due to the high pore volume of MIL-101(Cr). The CO2/CH4 selectivity increased from 54 to 89 from the neat 6FDA-mPD polymer to the 24 wt% MOF-199@6FDA-mPD membrane, apparently due to the high CO2 adsorption capacity of MOF-199.