The invention relates to a complex curved surface creation method for generating a curved surface in which roundness (ARC) of a radius R is provided at a portion where a first curve (11) approximated by straight lines on a first three-dimensional curved surface (1) intersects a second curve (12) approximated by straight lines on a second three-dimensional curved surface (2). Among line segments (P.sub.i P.sub.i-1) constituting the first curve (11) and line segments (P.sub.j P.sub.j+1) constituting the second curve (12), one line segment is selected from each curve in the order of their nearness to a point of intersection (P.sub.0) of the two curves. Next, it is determined whether a circular arc of radius R to which both of the line segments (P.sub.i P.sub.i-1, P.sub.j P.sub.j+1) are tangent exists. If such a circular arc does exist, the circular arc is inserted at the portion where the two curves intersect, thereby rounding the intersection. If such a circular arc does not exist, the next nearest line segments to the point of intersection (P.sub.0) are selected, similar processing is repeated and a circular arc is inserted at the portion where the two curves intersect, thereby rounding the intersection.