Abstract: In this paper, a new method is presented for cubic NURBS interpolating curve. The weights of the control vertices are calculated by quadratic programming and then all the control vertices are found by the method. The weights of the control vertices must be greater than zero if the weights Wi of the given data points are positive, and the interpolating curve meets C² continuity. When all of wi are equal to a positive constant, the NURBS interpolating curve will reproduce a nonuniform B-spline interpolating curve.