PURPOSE: To reduce the casting or oscillation mark on the surface while holding molten metal to the molten state by supplying heat on the surface zone of the molten metal in contact with the heat dissipating wall of a mold.

CONSTITUTION: In order to restrain the growth of solidified metal on the surface 3 of the molten metal 2 toward the inside of the mold 1 as less as possible and to make sure of fully filling of the covered molten metal 2 into a gap as much as possible, an induction heating device 9 in the mold wall 1 is disposed at the level of the molten metal surface 3 to supply the heat. The height of the induction heating device 9 is made to be from about 30 to 100 mm. During continuous casting, since the surface of the molten metal 2 is kept to the same level by continuously drawing a strand and continuously supplying the molten metal, the induction heating device 9 is fixedly disposed in the mold wall 1. In this way, the casting metal into the mold can be held to the molten state by supplying the heat into the zone of the molten metal surface adjoined to the mold wall.