Gas transport properties of BPPO, bromine modified (2,4-dimethyl-1,6-phenylene oxide or PPO), are measured. Three sizes of silica nanoparticles, 2 nm, 10 nm and 30 nm, are mixed with BPPO polymer at the weight ratio of 0.1, 0.2 and 0.3 to form BPPO/silica nanocomposite membranes. We found BPPO/silica nanocomposite membranes greatly enhance CO2 and O2 permeability while maintaining CO2/N2, CO2/CH4 and O2/N2 selectivity in relative to that of pure BPPO membranes. The membrane mechanical strength and stability, however, decrease sharply with the silica/BPPO weight ratio above 0.3. 10 nm size is found to show the best gas separation among the three particle sizes, with CO2 permeability of 808 Barrer and O2 permeability of 160 Barrer and CO2/N2 permselectivity of 21.0, CO2/CH4 permselectivity of 16.2, and O2/N2 permselectivity of 4.1, placing them close to or above Robeson's upper limit bound. It is identified that CO2/N2 separation mechanism is due to the solubility differences while diffusivity difference dominates CO2/CH4 separation. Both solubility and diffusivity differences play an equally important role in O2/N2 separation.