Abstract: A class of polyno mial blending functions of degree 4is presented.Based on the blending functions, we get a method of generating piecewise polyno mial curves with a shape parameter.By changing the value of the shape parameter, we can adjust the approaching degree of the curves to their control polygon and manipulate the curves to approxi mate the cubic unifor m B-spline curves fro m their both sides.For the given value of the shape parameter, the generated curves can be C² continuous and have the same ter minal properties as the cubic unifor m B-spline curves.So me co mputing examples of the curve design are given.