A membrane separation method for capturing carbon dioxide, in which a gas mixture is passed through a membrane unit to selectively separate the carbon dioxide, the membrane unit having a feed side, into which a carbon-dioxide-containing gas is provided, a retentate side, from which a carbon-dioxide-depleted stream is discharged, and a permeate side, from which a carbon-dioxide-enriched stream is produced, the membrane separation method comprising:
- a first separation step of passing the gas mixture through a first membrane unit;
- and
- a second separation step of passing the carbon-dioxide-enriched stream, withdrawn from the permeate side of the first membrane unit, through a second membrane unit,
- wherein the second separation step is performed at a temperature that is lower than a temperature at which the first separation step is performed.