A continuous casting apparatus for steel includes: a casting mold for casting a molten steel with a pair of long side walls and a pair of short side walls; a submerged entry nozzle which discharges the molten steel into the casting mold; and an electromagnetic stirring device which is disposed along each external surface of each of the long side walls and stirs an upper portion of the molten steel within the casting mold. A curved portion which is convexly curved toward the electromagnetic stirring device in plan view is formed at least at a position where the curved portion faces the submerged entry nozzle on each of the long side walls, and each of the long side walls including the curved portion has a uniform thickness. The shortest horizontal distance between a top which is a most depressed position when an internal surface of the curved portion is seen in plan view and an outer peripheral surface of the submerged entry nozzle is 30 mm to 80 mm in a range from a lower end portion of the electromagnetic stirring device to a position higher than an upper end portion thereof by 50 mm when viewed along a vertical direction.