A polymeric hollow fiber membrane is provided having a crosslinked selective layer formed by sequentially performing coating of a polymer precursor on a crosslinked polymeric hollow fiber membrane support and thermal condensation and thermal crosslinking thereof, a carbon molecular sieve hollow fiber membrane, methods for producing the same, and methods of separating gases using the same. The polymeric hollow fiber membrane and the carbon molecular sieve hollow fiber membrane each have a thin crosslinked selective layer and excellent plasticization resistance and separation performance. Accordingly, the polymeric hollow fiber membrane and the carbon molecular sieve hollow fiber membrane, each of which has a thin crosslinked selective layer, can be effectively used in the separation of a mixed gas.