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　Matlab7.0　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.