A combustion system (1,2,3,4,5,6) comprising: a separation portion that removes carbon dioxide from a treatment target gas containing a mixture gas containing methane as a main component and containing carbon dioxide to obtain methane gas of a high purity in which at least a content of carbon dioxide has been reduced; and a combustion portion that combusts the methane gas, wherein the separation portion includes a first treatment chamber (11, 36, 38) and a second treatment chamber (12, 37) separated from each other by a separation membrane therebetween, wherein the separation membrane selectively allows the carbon dioxide in the treatment target gas supplied to the first treatment chamber (11, 36, 38) to pass therethrough to the second treatment chamber (12, 37) to obtain a first separation gas having a higher methane purity than the treatment target gas in the first treatment chamber (11, 36, 38) and a second separation gas containing the carbon dioxide in the treatment target gas in the second treatment chamber, and wherein the separation membrane is a facilitated transport membrane to which a carrier that selectively reacts with carbon dioxide is added, wherein a) the facilitated transport membrane constitutes a gel layer with a water retentive hydrogel; and/or b)the combustion system comprisesa water vapor supply portion that supplies water vapor to the first treatment chamber (11, 36, 38), wherein the mixture gas containing the water vapor supplied by the water vapor supply portion is supplied to the first treatment chamber (11, 36, 38) as the treatment target gas. a separation portion that removes carbon dioxide from a treatment target gas containing a mixture gas containing methane as a main component and containing carbon dioxide to obtain methane gas of a high purity in which at least a content of carbon dioxide has been reduced; and a combustion portion that combusts the methane gas, wherein the separation portion includes a first treatment chamber (11, 36, 38) and a second treatment chamber (12, 37) separated from each other by a separation membrane therebetween, wherein the separation membrane selectively allows the carbon dioxide in the treatment target gas supplied to the first treatment chamber (11, 36, 38) to pass therethrough to the second treatment chamber (12, 37) to obtain a first separation gas having a higher methane purity than the treatment target gas in the first treatment chamber (11, 36, 38) and a second separation gas containing the carbon dioxide in the treatment target gas in the second treatment chamber, and wherein the separation membrane is a facilitated transport membrane to which a carrier that selectively reacts with carbon dioxide is added, wherein a) the facilitated transport membrane constitutes a gel layer with a water retentive hydrogel; and/or b)the combustion system comprisesa water vapor supply portion that supplies water vapor to the first treatment chamber (11, 36, 38), wherein the mixture gas containing the water vapor supplied by the water vapor supply portion is supplied to the first treatment chamber (11, 36, 38) as the treatment target gas. a) the facilitated transport membrane constitutes a gel layer with a water retentive hydrogel; and/or b)the combustion system comprisesa water vapor supply portion that supplies water vapor to the first treatment chamber (11, 36, 38),