To reduce an amount of an NOx generated by a flat flame burner by using a principle of a flame dilution to lower an oxygen partial pressure by lowering a temperature of a reaction zone.

The flat flame burner comprises at least one fuel injection tube and a combustion air supply tube provided along an axis of a burner body. In this case, fuel 21 is introduced into a combustion produced gas so as to conduct a first fuel dilution in the produced gas through one or a plurality of axial orifices provided near an outer surface of a combustion tunnel 9 by one or a plurality of injection tubes 18, 19. Mixed gas 23 of the obtained fuel- combustion produced gas is further diluted by combustion air 24.