Abstract: In order to improve contour controlling accuracy of Computer Numerical Control（CNC） system，the problem that control software of the system can directly output spline must be solved.Iterative relationship between parameters of two adjacent interpolation points on a Non-Uniform Rational B Spline（NURBS） curve is obtained based on Taylor formula.To B spline basis functions and their arbitrary order derivatives which need to be frequently calculated during interpolating a NURBS curve，a uniform calculating method of block matrix multiplying continuously is presented.Numerical calculation method is used to solve some relative problems such as curve’s length and so on during interpolating.The example demonstrated here indicates that the proposed method can be applied to actual CNC system.