To provide a combustor which can both efficiently and stably advance combustion reaction even at low temperatures by enlarging the surface area of a catalyst and fixing it with sufficient strength, and which can also reduce the usage of the catalyst.

A combustor 2 is such that fuel flow channels 3 are formed between stacked substrates 2a and 2a and the combustion catalyst 4 is located inside the fuel flow channels 3. The combustion catalyst 4 is made by baking a mixture of one or more kinds of metals or their compounds which will become catalytic active species, one or more kinds of oxide sols selected from among a silicon oxide sol and metal oxide sols, and one or more kinds of alkoxides selected from among silicon alkoxide and metal alkoxides.