Abstract: In this paper, an algorithm for constructing C-B-spline curve which is tangent to the given polygon is described. The control points of the C-B-spline to be constructed are computed simply by the vertices of the given tangent polygon. The constructed curves are shape-preserving to the tangent polygons. The local modification to the C-B-spline curve can be completed by simply adjusting the corresponding control parameters. Three examples are included.