A press-forming method for a component having a hat-shaped or U-shaped cross section and comprising a curved portion curved in a widthwise direction along with a longitudinal direction and straight side portions connecting to both ends of the curved portion from a sheet-shaped blank, wherein the blank is drawn to a hat-shaped or U-shaped cross section through a hat-shaped cross-sectional form having a top portion, vertical wall portions connecting at their upper end parts to both end parts of the top portion through fillet portions, and flange portions connecting at their internal end parts to the lower end parts of the vertical wall portions through fillet portions, and a material movement in the flange portion of the curved portion is caused in the drawing to mitigate tensile deformation or compression deformation in the circumferential direction generated in the flange portion of the curved portion.