In this paper, we propose a new method of contour error modeling for cross-coupled control of CNC machines. This modeling method is based on the information that the interpolator of a CNC machine generates knot points per each sampling time in order to approximate a given curved path as a series of small straight-line segments. The merits of the proposed method are : (1) its applicability for arbitrary curved contours and (2) its ability to calculate contour errors more accurately than the other conventional methods. The proposed method is evaluated and compared with the conventional methods using the three typical curved trajectories by computer simulations. Furthermore, it is shown that the cross-coupled controller based on this proposed error model improves contouring accuracy more effectively than the other methods.