Based on the principle of parametric curve paths CNC interpolating, it is pointed out that the Taylor series methods and “Parameter-Arc-length” curve fitting methods for CNC curved path interpolation are not perfect in theory. Thus a novel curved path interpolation method is proposed with Newton iteration functions. The detailed realization of the proposed algorithm has also been given. It has many advanced features, such as good stability, fast convergence, low computational effort and high precision. Simulations and experimentations show that the proposed algorithm can reduce the feedrate fluctuation by 10²-10⁷times with equal or little more computational effort comparing with Taylor series methods.