The present invention relates to a low-temperature membrane separation device and method for capturing carbon dioxide at a high concentration, in which a gas mixture is passed through a membrane unit to thus separate carbon dioxide. The membrane unit includes a membrane for capturing carbon dioxide and is connected to a feed gas line, a retentate gas line and a permeate gas line. The method includes a first separation step of passing the gas mixture through a first membrane unit and a second separation step of passing the permeation gas, which is discharged to the permeate gas line connected to the first membrane unit, through a second membrane unit. The second separation step is performed at a temperature that is lower than a temperature at which the first separation step is performed.