Abstract: Numeric control machining and on-line compensation for aspheric surface are key techniques in ultra-precision machining.In this paper,conformal cubic NURBS interpolating curve is applied to fit the character curve of aspheric surface.To evaluate the performance of the conformal cubic NURBS interpolation,a algorithm and its process are also proposed and imitated by MatlabT.0 software.The result verifies that this method can ensure smoothness of interpolating spline curve and preserve the characters original shape.The surface quality interpolated by cubic NURBS is higher than that by line or circle.The algorithm is beneficial to increasing the surface form precision of workpieces in ultra-precision machining.