Abstract: By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the uniform B-spline curve.The generalized B-spline curve is denoted as αExtension B-spline curve,whose shape-control capability is shown to be much better than that of B-spline curve.The representation and properties of the extension curve is studied.The curve is easy and intuitive to reshape by varying the parameters；so it is useful in some applications of CAD/CAM.