A hat-shaped cross-section component manufacturing apparatus includes: a die that includes a forming face that grips and presses a metal stock sheet; a blank holder, that includes a forming face that grips and presses the metal stock sheet so as to configure a forming face corresponding to the forming face of the die, a pad that is disposed inside the opening formed in the die, and that includes a forming face that grips and presses the metal stock sheet; and a punch that is disposed facing the pad and that includes a forming face that grips and presses the metal stock sheet so as to configure a forming face corresponding to the forming face of the pad. The hat-shaped cross-section component manufacturing apparatus further includes a pressure limiting device that limits a formed curving component from being pressed between the pad and the blank holder during demolding.