The present invention discloses a new type of polyimide membranes including hollow fiber and flat sheet membranes with high permeances for air separations and a method of making these membranes. The new polyimide hollow fiber membranes have O2 permeance higher than 300 GPU and O2/N2 selectivity higher than 3 at 60° C. under 308 kPa for O2/N2 separation. The new polyimide hollow fiber membranes also have CO2 permeance higher than 1000 GPU and single-gas selectivity for CO2/CH4 higher than 20 at 50° C. under 791 kPa for CO2/CH4 separation.