Abstract: Guide roller units are made movable back and forth in the direction of thickness of a slab, allowing slab lagging covers to be inserted to and withdrawn from gaps formed between the guide roller units and the slab. Depending on the casting speed, those ones of the guide roller units and the slab lagging covers which are in proper positions are replaced from one to the other for selective use so that the respective lengths of a cooling zone and a heat keeping zone are adjusted to control the cooling rate of the slab in a positive manner. The slab temperature can be kept at a value capable of carrying out rolling regardless of change in the casting speed depending on variations in the amount of molten steel supplied.