A furnace-heating combustion apparatus that allows adjustment of a ratio between the amount of primary air and the amount of secondary air. A double-tube elongate burner extends through a rear wall portion of an air box disposed away from a furnace wall. The leading end portion of the burner is disposed inside a tube section such that a secondary air conduit is formed between an outer circumferential face of the leading end portion and an inner circumferential face of the tube section. A primary air conduit is provided at the leading end portion of the burner to introduce the air inside the air box from the rear end portion and cause it to flow toward the leading end portion. A burner supporting means is provided for to allow adjustment of the position of the burner in the longitudinal direction relative to the rear wall of the air box.