This invention relates to aromatic block copolyimide polymers comprising both hydroxyl functional groups and carboxylic acid functional groups, their membranes and methods for making and using these polymers and membranes. The aromatic block copolyimide polymer described in the present invention comprises both hydroxyl functional groups and carboxylic acid functional groups. The gas transport properties particularly the selectivities of the aromatic block copolyimide comprising both hydroxyl functional groups and carboxylic acid functional groups were significantly improved compared to those of the aromatic random copolyimide comprising both hydroxyl functional groups and carboxylic acid functional groups.