A gas separator includes a separation membrane complex in which a separation membrane with pores having a mean pore diameter less than or equal to 1 nm is formed on a porous support, and a gas supply part that supplies a mixed gas including CO2 and another gas from the side of the separation membrane to the separation membrane complex. Then, CO2 in the mixed gas is caused to permeate through the separation membrane and the support and is separated from the mixed gas in a state in which at least part of a permeation surface of the support, from which a gas having permeated through the separation membrane is exhausted, has a temperature lower by 10° C. or more than the temperature of the mixed gas before being supplied to the separation membrane complex.