Abstract: The paper constructs a new extended curve——BH-Bézier curve with Bézier curve,H-Bézier curve and weight theory and presents the properties of its basis function and BH-Bézier curve.The geometric continuity problems between the cubic BH-Bézier curves are studied,thus the corresponding theorems of the G⁰,G¹,G² continuity and their corollaries are obtained,and some of their practical applications are given.