The carbon dioxide membrane separation system in a coal gasification process contains introduction of a mixed gas of hydrogen (H2) and carbon dioxide (CO2) in a high temperature and high pressure condition generated through water gas shift reaction from a water gas shift reaction furnace, while maintaining the temperature and pressure condition, to a zeolite membrane module containing a zeolite membrane for removing carbon dioxide, thereby removing carbon dioxide and generating a fuel gas rich in hydrogen. The fuel gas rich in hydrogen in a high temperature and high pressure condition discharged from the zeolite membrane module is fed to a gas turbine of the power generation facility while maintaining the temperature and pressure condition.