In a mold for casting a billet with a curved type continuous casting apparatus, D0 (m) is an inner diameter at a lower mold edge and R0 (m) is a curvature radius of an outer curvature side at the lower mold edge. When a rate of change Tp (%/m) in mold inner diameter per unit length along a casting direction is Tp=(1/D0)×(dD/dx)×100 (%/m), and when a rate of change Rp (%/m) in curvature radius of an outer curvature side per unit length along the casting direction is Rp=(1/R0)×(dR/dx)×100 (%/m), the rate of change Tp in mold inner diameter and the rate of change Rp in curvature radius satisfy a relationship expressed Rp=(Tp/2)×(D0/R0), where D is a mold inner diameter at a distance x away from an upper mold edge and R in Formula 2 is a curvature radius of the outer curvature side at the distance x.