Disclosed herein is a composite hollow fiber polymer membrane including a porous core layer and a selective sheath layer. The porous core layer includes a polyamide-imide polymer, or a polyetherimide polymer, and the selective sheath layer includes a polyimide polymer, which is prepared from monomers A, B, and C. The monomer A is a dianhydride of the formula
wherein X1 and X2 are independently halogenated alkyl group, phenyl or halogen and R1, R2, R3, R4, R5, and R6 are independently H, alkyl, or halogen. The monomer B is a diamino cyclic compound without a carboxylic acid functionality and the monomer C is a diamino cyclic compound with a carboxylic acid functionality. The polyimide polymer further includes covalent ester crosslinks. Also disclosed herein is a method of making the composite polymer membrane and a process for purifying natural gas utilizing the composite polymer membrane.