A hat-shaped cross-section component manufacturing apparatus includes: a die that includes a forming face that presses both side portions of a metal stock sheet; a punch that includes a forming face that presses a central portion of the metal stock sheet; a pad that includes a forming face that presses and grips the central portion of the metal stock sheet against the punch; and a blank holder that includes a forming face that presses and grips the both side portions of the metal stock sheet against the die. The hat-shaped cross-section component manufacturing apparatus further includes a pressure limiting device configured including a floating block that moves together with the blank holder when forming of a curving component has been completed, that is interposed between the pad and the blank holder, and that limits pressing of the formed curving component between the pad and the blank holder during demolding.