PURPOSE: To surely execute the continuous casting, in which large scale rolling reduction equipment is unnecessary and surface flaw on a cast slab is not developed and the center segregation is prevented.

CONSTITUTION: In order to forcedly develop bulging in the cast slab 5, 6 just below the mold 1 in a continuous casting apparatus, the recessed part is formed in the casting direction at the center zone of the inner wall of a long side in a cooling grid part 2. Further, at the same time, the light rolling reduction is applied to the cast slab 5, 6 by small diameter roll group 4 forming the convex crown in at least one of the roll in one pair of the rolls forcedly arranged while inserting the cast slab 5, 6 near the crater end 7. Then, the continuous casting, in which the large scale rolling reduction equipment is unnecessary because of light rolling reduction and the surface flaw on the cast slab, such as longitudinal crack, traversing crack, is not developed and the center segregation is prevented, is surely executed.