Abstract: In view of the deficiency of the transition curve and surface construction methods in the shape blending, a method for constructing transition curve and surface based on curve models with parameters is presented in this paper. First, a blending function with a parameter is constructed by using a class of curve model with parameters. Then, construction of the transition curve based on the presented blending function is studied, and construction of the optimal transition curve based on energy optimization method is discussed. Finally, construction of the transition surface is similarly discussed. Example results show that, the two transited curves and surface can be arbitrary parametric curves and surfaces when the blending function is used to construct transition curve and surface. The transition curves and surfaces are not only quasi C² continuous on the boundary, but also can achieve shape adjustment by the parameter of the blending function.