A continuous casting apparatus continuously casts an ingot formed of titanium or a titanium alloy. The apparatus includes a bottomless mold with a circular cross-sectional shape and a plasma torch. In the bottomless mold, a molten metal is poured from a top opening and the molten metal is solidified and the molten metal solidified is pulled out downward. The plasma torch is disposed on an upper side of the molten metal in the mold and generates a plasma arc that heats the molten metal. A plurality of plasma torches are disposed on the upper side of the molten metal in the mold. The plurality of plasma torches are moved in a horizontal direction above a melt surface of the molten metal along a trajectory keeping a distance not to allow for interference with each other.