Abstract: A molten Mg or Mg alloy is supplied into a mold, which is sheltered from the surroundings, from a pool in a tundish, which is shielded from the surroundings. An Mg slab or Mg alloy slab in the mold is drawn out to the outside from an outlet of the mold. A cooling medium is jetted onto the slab on an outer side of and in a vicinity of the outlet to cool the slab. A sealing gas is sprayed over an entire width of a free surface of the molten Mg or Mg alloy on an inner side of and in the vicinity of the outlet, to seal a portion above the entire width of the free surface of the molten Mg or Mg alloy, whereby preventing oxygen from flowing into the mold from the portion and preventing the cooling medium from running back to the mold side.