A hat shaped cross-section component manufacturing method comprising: a supporting process of disposing a semi-finished formed component (10; 501; 100; 110; 120; 130; 140; 150; 70; 700) with a hat-shaped cross-section between a restriking punch and a restriking die that are disposed facing each other, and supporting a top plate (11; 501c; 102; 112; 122; 132; 142; 152; 702) of the semi-finished formed component from the restriking punch side using a support member extending from the restriking punch toward the restriking die side; characterized by: a positioning process of housing the top plate inside a first recess portion configuring a top face side of a forming recess that is formed to the restriking die and that is open toward the restriking punch side, gripping the top plate using the support member and the restriking die, and positioning the semi-finished formed component in a width direction using the first recess portion and a pair of vertical walls (12a,b; 104, 106; 114, 116; 124a,b; 134, 136; 144, 146; 154, 156; 501a,b; 704a,b) that extend from both width direction ends of the top plate of the semi-finished formed component; and a restriking process of inserting the restriking punch inside a second recess portion configuring an opening side of the forming recess and set with a larger width dimension than the first recess portion, and restriking the semi-finished formed component using the restriking punch and the restriking die. a supporting process of disposing a semi-finished formed component (10; 501; 100; 110; 120; 130; 140; 150; 70; 700) with a hat-shaped cross-section between a restriking punch and a restriking die that are disposed facing each other, and supporting a top plate (11; 501c; 102; 112; 122; 132; 142; 152; 702) of the semi-finished formed component from the restriking punch side using a support member extending from the restriking punch toward the restriking die side; characterized by: a positioning process of housing the top plate inside a first recess portion configuring a top face side of a forming recess that is formed to the restriking die and that is open toward the restriking punch side, gripping the top plate using the support member and the restriking die, and positioning the semi-finished formed component in a width direction using the first recess portion and a pair of vertical walls (12a,b; 104, 106; 114, 116; 124a,b; 134, 136; 144, 146; 154, 156; 501a,b; 704a,b) that extend from both width direction ends of the top plate of the semi-finished formed component; and a restriking process of inserting the restriking punch inside a second recess portion configuring an opening side of the forming recess and set with a larger width dimension than the first recess portion, and restriking the semi-finished formed component using the restriking punch and the restriking die. a positioning process of housing the top plate inside a first recess portion configuring a top face side of a forming recess that is formed to the restriking die and that is open toward the restriking punch side, gripping the top plate using the support member and the restriking die, and positioning the semi-finished formed component in a width direction using the first recess portion and a pair of vertical walls (12a,b; 104, 106; 114, 116; 124a,b; 134, 136; 144, 146; 154, 156; 501a,b; 704a,b) that extend from both width direction ends of the top plate of the semi-finished formed component; and a restriking process of inserting the restriking punch inside a second recess portion configuring an opening side of the forming recess and set with a larger width dimension than the first recess portion, and restriking the semi-finished formed component using the restriking punch and the restriking die.