Abstract: An apparatus for continuous casting of magnesium billets or slabs using an electromagnetic field, and a method thereof compensates small solidification latent heat of magnesium, controls a solidification speed, and stirs molten metal within a mold via an electromagnetic field, thereby enabling continuous casting. The apparatus comprises a mold for continuous casting an as-cast billet or slab, a coil positioned outside the mold and adapted to allow electric current to be applied thereto, and a cooling nozzle positioned outside the mold and the as-cast billet or slab. During casting, electric current having a frequency of 2˜1,000 D or electric current of 50˜10,000 A having a frequency of 200˜200,000 D is applied to the coil. A magnesium billet or slab having enhanced inner quality can be produced at a high casting speed without surface defects by applying a low frequency or high frequency electromagnetic field to the mold during continuous casting of magnesium.