Supported Mixed Matrix Membrane (SMMM) Polyether block amide/nanoclay (PEBA/Cloisite 30b), based on Polyacrylonitrile on nonwoven Polyester (PAN/PE), was fabricated by the spin coating method, following optimization of fabrication conditions for Single-Layer Mixed Matrix Membranes (SLMMMs). Cloisite 30b is a type of montmorillonite modified from nanoclays family. The fabricated membranes were examined structurally through The X-ray Diffraction (XRD), The Field Emission Scanning Electron Microscopy (FESEM), The Fourier-transform infrared spectroscopy (FTIR), and The Atomic force microscopy (AFM) analyses, and evaluated operationally by conducting permeability tests of the pure gases of CO2, CH4 and N2. The effect of different Cloisite 30b loadings and the varying pressures on the gas separation performance of the membranes was investigated. Elevation of the loading up to 0.2 wt% Cloisite 30b increased the permeability and the selectivity, whereas further increase up to 1 wt% reduced the permeability and selectivity. After an increase in pressure from 4 to 14 bar, an elevated permeability and selectivity was observed. The membrane with a Cloisite 30b loading of 0.2 wt% had the best performance in the separation of the pure gases of CO2, CH4, and N2 such that the permeability of CO2, along with the selectivity of CO2/N2, and CO2/CH4 had increase of about 55.55%, 26.45% and 38% in comparison with the Single Layer Neat Membrane (SLNM). The permeability of CO2, the selectivity of CO2/N2, and the selectivity of CO2/CH4 of SMMM with a Cloisite 30b loading of 0.2 wt% also indicated an increase of about 364%, 18% and 47.8% in comparison to the Supported Neat Membrane (SNM). Furthermore, CO2 permeability through SMMM with cloisite30b loading of 0.2 wt% indicated a growth of about 562.5% in comparison to SLMMM with the same loading.