In this work, novel mixed matrix membranes (MMMs) were fabricated by incorporation of octatrimethylsiloxy polyhedral oligomeric silsesquioxane (POSS) and fumed silica (FS) as nanoparticle fillers into poly(ether-block-amides) (Pebax2533) as polymer matrix in order to carbon capture and remove acid gas from natural gas. Fourier transforms infrared (FTIR) spectroscopy proved the chemical structure of the nanocomposites and field-emission scanning electron microscopy (FESEM) unveiled the appropriate filler dispersion and adhesion between fillers and polymer. Thermogravimetric analysis (TGA) showed that all the samples have reasonable thermal stability which is enhanced by nanoparticles. The permeability and selectivity of pure CO2, CH4, and N2 gases were measured in the 4–10 bar pressure difference range. The incorporation of studied nanoparticles caused improve performance including the permeability and selectivity relative to the neat Pebax. In 4 bar and 0.1 wt% POSS, CO2 permeability raised by 87%, while the highest increase in CO2/CH4 selectivity is at 2 wt% POSS. The gas transport and free volume were also interpreted by densitometry showing that the addition of the fillers had a positive effect on the free volume and chain packing of the polymeric membranes.