Liquid carbon dioxide separated from sour gas is expanded by throttling decompression and is gas-liquid separated at a low temperature so as to be supplied for shipping or the improvement of petroleum recovery. Methane generated from a stranded gas well is allowed to pass as a coolant through liquid carbon dioxide separated and discharged from sour gas generated from the stranded gas well so as to cool liquid carbon dioxide. Disclosed is a module for treating carbon dioxide, and a treatment method thereof for supplying liquid carbon dioxide at a proper temperature and state conditions when there is a need for liquid carbon dioxide of very low temperature for the storage or collection of carbon dioxide, the improvement of petroleum recovery, or the like by cooling carbon dioxide using a material separated from sour gas of a stranded gas well as a coolant.