Abstract: This paper extends a given cubic Bézier curve to another nonadjacent one using one or two cubic Bézier curves to connect them with some geometric continuous conditions.The extension curves are constructed by the geometric continuous conditions by minimizing some fairing functions based on the shortest arc-length,minimum energy and minimum curvature variation of the curves respectively.Shape parameters are introduced in the process of optimization and can be adjusted by the user to control the shape of the extension curves.