A method of continuously casting a molten metal, capable of minimizing the unstability of initial solidification of a molten metal and stably attaining the improvement of the performance of being lubricated of a cast piece and the property of the surface thereof, and an apparatus for embodying the method. A method of continuously casting a molten metal, wherein a molten metal is poured into a mold, which is vibrated or not vibrated in a predetermined mode, with an alternating current supplied to an electromagnetic coil provided so as to surround a wall of the mold or an electromagnetic coil buried in a side wall thereof, continuous casting being carried out as an electromagnetic force is applied to the molten metal which is about to start being solidified, characterized in that the amplitude or waveform of the alternating current supplied to the molten metal is varied periodically; and an apparatus for embodying the method.