PURPOSE: To enable the cooling control corresponding to a kind of steel and to restain the occurrence of surface defect in a continuously cast slab by arranging small holes on the surface of a plating layer of the cooling plate surface on a continuous casting mold for steel having plural heating members and thermometers.

CONSTITUTION: The sheath type heaters 5 and thermocouples 6 are arranged at a meniscus position in the mold and the small holes 8 are bored on the plating layer 7 in the meniscus range on the mold surface and further, warm water 9 is used as a cooling medium. The temp. gradient in the cooling plate is varied by locally heating in the cooling plate on, the mold with the sheath type heaters 5 arranged at the meniscus position in the mold to reduce heat flow flux flowed from molten steel 4. The heating quantity of the heater 5 is controlled based on the temp. measured result with the thermocouples 6 and varied in the casting direction and the width direction of the mold so as to become the optimum heat flow flux corresponding to the kind of steel for casting. Further, the small hole plating layer 8 applied near the meniscus on the mold surface promotes slow cooling effect, and also primary dendritic arm interval is made to be small by making the small holes the starting points in the formation of solidified structure.