The key challenge in the synthesis of composite mixed matrix membrane (MMMs) is the incompatible membrane fabrication using porous support in the dry-wet phase inversion technique. The key objective of this research is to synthesize thin composite ternary (amine) mixed matrix membranes on microporous support by incorporating 10 wt% of carbon molecular sieve (CMS) and 5-15 wt% of diethanolamine (DEA) in polyethersulfone (PES) dope solution for the separation of carbon dioxide (CO2) from methane (CH4) at high-pressure applications. The developed membranes were evaluated for their morphological structure, thermal and mechanical stabilities, functional groups, as well as for CO2-CH4 separation performance at high pressure (10-30 bar). The results showed that the developed membranes have asymmetric structure, and they are mechanically strong at 30 bar. This new class of PES/CMS/DEA composite MMMs exhibited improved gas permeance compared to pure PES composite polymeric membrane. CO2-CH4 perm-selectivity enhanced from 8.15 to 16.04 at 15 wt% of DEA at 30 bar pressure. The performance of amine composite MMMs is theoretically predicted using a modified Maxwell model. The predictions were in good agreement with experimental data after applying the optimized values with AARE % = ∼less than 2% and R2 = 0.99.