The part’s precision-machined quality of NC machining is influenced by the chord error greatly during precision machining. The confined chord error Algorithm for Machining Complex Parametric Curve is proposed for the complexity of the chord error. The information of the arc length error is utilized to control the chord error of the interpolated point indirectly. The arc length error of interpolated point is computed by Simpson expressions, the information of coordinate and the first order derivative of interpolated point is computed by the interpolation algorithm, so the computed difficulty is not increased greatly. The computed error of the algorithm is discussed and the simulation example of NURBS curve proves that the destined precision of the chord error can be satisfied by this algorithm.