A continuous casting machine and method using molten mold flux, wherein the continuous casting machine includes a mold cover for covering an upper portion of a mold; a mold flux melting unit for melting mold flux to be supplied into the mold; and a mold flux delivery unit for supplying the mold with the molten mold flux melted in the mold flux melting unit, wherein the delivery unit includes an injection tube with one end connected to the mold flux melting unit and the other end positioned in the mold through the mold cover, and an injection tube heater for heating the injection tube. Since a slag bear continuous casting machine and method using molten mold flux is removed, the consumption of mold flux is greatly increased compared with the case of a conventional casting work, so that the friction between a mold and a solidified shell is reduced. As a result, an amount of scarfing of a cast piece is greatly reduced and no carbon pick-up occurs.