A continuous heating apparatus which can maintain an appropriate hating of strip material the as much as possible even if a remaining amount of looper is reduced, and which can reliably decrease the furnace temperature to a temperature equal to or less than the safety temperature controls the combustion amounts in the combustion segments respectively so that internal temperatures of the combustion segments are maintained at respectively predetermined preset temperatures if the surplus time is longer than a predetermined preset time, and varies the combustion amounts in the combustion segments respectively in a predetermined profile with respect to the surplus time if the surplus time is shorter than a predetermined preset time.