To investigate effects of the frequency parameter on the curve shape, this paper analyzes the shape features of the cubic ω-Bézier curve by using the method based on the theory of envelope and topological mapping. Necessary and sufficient conditions are derived for this curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions are completely characterized by the vertex of the control polygon and frequency parameter. Furthermore, it discusses the influences of frequency parameter on the shape diagram and the ability for adjusting the shape of the curve.