Disclosed is a continuous casting method in which a melt obtained by melting titanium or a titanium alloy is poured into a bottomless mold and is drawn downward while being solidified, wherein: the surface of the melt in the mold is heated by horizontally moving a plasma torch over the surface of the melt; thermocouples are provided at a plurality of locations along the circumferential direction of the mold; if the temperature of the mold measured by one of the thermocouples is lower than a target temperature, then the output of the plasma torch is increased when the plasma torch comes close to the location where that thermocouple is installed; and if said temperature is higher than the target temperature, then the output of the plasma torch is decreased when the plasma torch comes close to the location where that thermocouple is installed.