NOVELTY - A composite hollow fiber polymer membrane comprises a porous core layer comprising polyamide-imide polymer, and selective sheath layer on the core layer comprising polyimide polymer which is prepared using monomer (A), monomer (B) and monomer (C). The monomer (A) is dianhydride (I). The monomer (B) is diamino cyclic compound without carboxylic acid functionality. The monomer (C) is diamino cyclic compound with carboxylic acid functionality. The polyimide polymer comprises covalent ester crosslink.    USE - Composite hollow fiber polymer membrane is used for purifying natural gas (claimed).    ADVANTAGE - The composite hollow fiber polymer membrane has excellent open porous morphology, compatibility, plasticization resistance and thermal stability, and is free from defects. The natural gas purified using the composite hollow fiber polymer membrane by efficient and economical process with high productivity.    DETAILED DESCRIPTION - A composite hollow fiber polymer membrane comprises a porous core layer comprising polyamide-imide polymer, and selective sheath layer on the core layer comprising polyimide polymer which is prepared using monomer (A), monomer (B) and monomer (C). The monomer (A) is dianhydride of formula (I). The monomer (B) is diamino cyclic compound without carboxylic acid functionality. The monomer (C) is diamino cyclic compound with carboxylic acid functionality. The polyimide polymer comprises covalent ester crosslink.    X1,X2=halogenated alkyl, phenyl or halo;and    R1-R6=H, alkyl, or halo.    INDEPENDENT CLAIMS are included for the following:    (1) preparation of composite hollow fiber polymer membrane, which involves extruding porous core layer comprising polyamide-imide polymer and selective sheath layer; and    (2) process for purifying natural gas, which involves providing a natural gas stream comprising at least one impurity to at least one membrane unit comprising composite polymer membrane to form an impurity-rich permeate and an impurity-depleted product gas stream, and recovering the impurity-depleted product gas stream. The composite polymer membrane comprises the composite hollow fiber membrane.