Freeform curve is often encountered during the numercial control (NC) machining of configuration contour profile of workpieces, but the common NC system only has linear interpolation and circular interpolation function. For directly machining of a freeform curve, a straight line or arc could only be used to approximate the knot and to perform the approximation tool machining process. The method of equalerror approximation was one of the effective methods for linear approximation knot creation, which could make equalerror for all approximation line segment. In the study of the equalerror linear knot approximation, a new calculation method was put forward for the equalerror linear approximation based on geometric operations. A mathematical model of freeform curve was established by this method, through the Particle Swarm Optimization (PSO) computation to iteratively calculate the cutter location coordinates information for the freeform curve. Through the VC++ programming tool, the method is implemented for development of the equalerror linear approximation for the freeform curve of NC system, which is verified through an example for effectiveness of its algorithm.