A method and apparatus manufactures a closed structure part without flange having a curvature and welded edges along a longitudinal direction of the part and further having a varying cross-sectional shape, from two metal plates. Each of two metal plates provided with a curvature along the longitudinal direction of the plate and provided with both ends in a width direction of the plate, are press-formed such that a folding line is formed at positions corresponding to a non-welded bent edge in a cross section of the part, and stacked on each other vertically such that their bulging sides face outward. Their left ends and right ends in the width direction are mutually welded along the longitudinal direction to form welded edges.