Graphene Oxide (GO) dispersed in a polymer blend of Polystyrene (PS)/Poly (methyl methacrylate) (PMMA) nanocomposite membranes have been prepared by the solution cast method for hydrogen gas permeation application. This paper reports a study of blends of PMMA and PS that were prepared in different ratios of weight percentage for PMMA: PS (80:20, 50:50 and 60:40) composite with 1 wt% of GO and 2 wt% of GO. The structural and morphological properties of these prepared composite membranes have been characterized using gas permeation, Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS). UV Spectroscopy and FT-IR have carried out the optical absorbance measurement of the composite membranes. The permeability measurements indicate that the GO nanofillers in blends of PS/PMMA have shown higher permeability for hydrogen gas than that of pure polymers. The gases used for the permeation measurements were H2, CO2, N2 and CH4. Selectivity has been calculated for H2/CO2, H2/N2 and H2/CH4 gas pairs and plotted to show Robeson's 2008 upper bound and compared with reported data. The transport properties of these gases have been compared with that of a neat membrane. The permeability of all gases has increased to that of the unmodified polymer membrane. The selectivity measurements show that GO composite with PS/PMMA blend membranes is highly selective for hydrogen gas from different gas pairs, therefore, these composite membranes can be used for hydrogen purification. There is a trade-off between permeability and selectivity parameters; GO nanofillers keep selectivity constant as permeability increases, which the nanogap theory could explain.