To solve the problem of stable reduction combustion being not alway obtained in actual operation, because air for complete combustion is always fed in a constant volume in a reduction combustion method, where reduction combustion is effected in a furnace to perform non-oxidation heating of a substance to be heated and reduce the generation of NOx, and air for complete combustion is introduced to a burner on the exhaust side to cause complete combustion of unburnt contents in a regenerative burner system.

In the regenerative burner system, second oxidant feed routes 19a and 19b are connected to respective burners 3a and 3b; respective governors 20a and 20b are situated in the oxidant feed routes; by connecting pipes 21a and 21b for control to fuel feed routes 13a and 13b for the other burners 3b and 3a, a flow rate of an oxidant fed through the second oxidant feed routes is made to be in proportion, based on a flow rate of an fuel fed to the space part through the fuel feed routes; and such a constituted reduction combustion mechanism is proposed, and the second oxidant feed route can be branched from oxidant feed routes 6a and 6b of a burner on the other side.