•High pressure CO2/CH4 separation of the optimized MMMs with CO2-philic MOFs.•Simulating an actual natural gas separation condition (pressure, feed, temperature).•At highest pressure, the effect of H2S (50,000 ppm) in feed was investigated.•MMMs showed CO2- and H2S-induced plasticization suppression.•Revealed reversible competitive sorption, also increased total acid gas selectivity. The gas separation properties of 6FDA-DAM mixed matrix membranes (MMMs) with three types of zirconium-based metal organic framework nanoparticles (MOF NPs, ca. 40 nm) have been investigated up to 20 bar. Both NPs preparation and MMMs development were presented in an earlier publication that reported outstanding CO2/CH4 separation performances (50:50 vol% CO2/CH4 feed at 2 bar pressure difference, 35 °C) and this subsequent study is to demonstrate its usefulness to the natural gas separation application. In the current work, CO2/CH4 separation has been investigated at high pressure (2–20 bar feed pressure) with different CO2 content in the feed (10–50 vol%) in the temperature range 35–55 °C. Moreover, the plasticization, competitive sorption effects, and separation of the acid gas hydrogen sulfide (H2S) have been investigated in a ternary feed mixture of CO2:H2S:CH4 (vol% ratio of 30:5:65) at 20 bar and 35 °C. The incorporation of the Zr-MOFs in 6FDA-DAM enhances both CO2 permeability and CO2/CH4 selectivity of this polymer. These MMMs exhibit high stability under separation conditions relevant to an actual natural gas sweetening process. The presence of H2S does not induce plasticization but increases the total acid gas permeability, acid gas/CH4 selectivity and only causes reversible competitive sorption. The overall study suggests a large potential for 6FDA-DAM Zr-MOF MMMs to be applied in natural gas sweetening, with good performance and stability under the relevant process conditions.