The invention of polymers of intrinsic microporosity (PIMs) has opened up great opportunities for the developments of high-performance composite membranes which possess both high gas permeance and selectivity. However, it still remains challenging to translate such PIM materials into PIM-related composite membranes with characteristics of high permeance and selectivity. For the first time, we report defect-free PIM composite hollow fiber membranes that have pure O-2 and CO2 permeances of 69 and 483 GPU, respectively, and O-2/N-2 and CO2/N-2 selectivities of 3.2 and 22.5, respectively. The O-2/N-2 and CO2/N-2 selectivities are further increased to 4.2 and 29.5 respectively in air separation and flue gas tests. The composite hollow fiber membranes consist of three layers. The top selective-layer material is made from the nucleophilic substitution copolymerization between PIM and beta-cyclodextrin (beta-CD) (referred to as PIM-CD), while the gutter and substrate materials are polydimethylsiloxane (PDMS) and polyacrylonitrile (PAN), respectively. The key to producing such composite membranes is to introduce a cross-linked PDMS gutter layer between the PIM-CD selective layer and PAN substrates that can (1) mitigate the detrimental solvent effects during the dip coating, (2) allow PIM to adhere on it, and (3) redistribute the gas transport across the membranes.