In this study, the separation of acid gases H2S and CO2 from N-2 and CH4 by pristine polymeric membranes including poly(amide-b-ethyleneoxide) (Pebax-1657), poly(acrylonitrile) (PAN) and poly(trimethylsilyl) propyne (PTMSP) have been studied by utilizing molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulation methods. The results indicated that, while the selectivity of the pristine Pebax membrane, for these gases, was higher than those of pristine PAN and PTMSP membranes, its permeability was lower. To obtain polymeric membrane with higher permeability, composite polymeric membranes (CPMs) consisting of [Pebax-1657 + PAN] and [Pebax-1657 + PTMSP + PAN] were constructed. However, the results indicated that the CPMs had low selectivity, in comparison to pristine Pebax membrane, for the binary gas mixtures. Therefore, to increase the CPMs' selectivity along with their permeability, the nano-filler zeolitic imidazole framework (ZIF-7) were added to the Pebax-1657 matrix of CPM with the optimum amount of 22 wt%, where the resulting nanocomposite polymeric membranes (NCPMs) indicated more significant separation efficiency (higher; diffusivity, solubility, permeability and selectivity). The physical properties of the simulated polymeric membranes such as density, glass transition temperature and fractional free volume were evaluated and the mechanisms involved in the gas separation, by the studied polymeric membranes, were discussed in the light of the obtained results, where their agreement with the available experimental data validated the simulation procedures as utilized in this study.