Abstract: H-Bézier curves,as a new kind of curve modeling tool,are presented in this paper, aiming at extending the representation of curves and surfaces．Based on the analysis of the properties of cubic H-Bézier curves,a subdivision algorithm is proposed to compute the control parameters and control points of the two subcurves p_t^* （t）（0≤t≤t^*） and p_α-t^* （t）（0≤t≤α-t^* ） subdivided by anypoint p（t^*）（0≤t^* ≤α） of cubic H-Bézier curves．The connection conditions between cubic H-Bézier curves and cubic Bézier curves are derived the applications of cubic H-Bézier curves in the surface modeling are given．The obtained results,which are simple and intuitionistic,can effectively improve the shape representation and control of cubic H-Bézier curves．