A water-cooled mold for use in continuous steel casting process has at least two vertically-spaced coils arranged in the wall structure of the mold so as to surround molten steel in the mold or in a solidification shell within the mold and such that a jet of molten steel from an immersion nozzle of a tundish in the molten steel collides with the mold wall at a level between the coils. During supplying the molten steel from the tundish into the mold, the coils are supplied with DC currents of opposite directions so as to generate cusp fields in the mold, thereby suppressing the movement of the jet of the molten steel, as well as ascending and descending flows of the molten steel after collision with the mold wall.