For continuously casting an ingot of titanium or titanium alloy, molten titanium or titanium alloy is poured into a top opening of a bottomless mold with a circular cross-sectional shape, the solidified molten metal in the mold is pulled downward from the mold, a plurality of plasma torches disposed on an upper side of molten metal in the mold such that their centers are located directly vertically above the molten metal in the mold, are operated to generate plasma arcs that heat the molten metal in the mold, and the plasma torches are moved in a horizontal direction above a melt surface of the molten metal in the mold, along a trajectory located directly vertically above the molten metal in the mold, while keeping a mutual distance between the respective plasma torches such that the plasma torches do not interfere with each other.