An algorithm to approximate a planar NURBS curve by ellipse-arc and bi-ellipse-arc is presented. The piecewise ellipse-arc spline calculated by this algorithm is G¹ continuous, and shape preserving. Compared with the present arc-approximation, this algorithm does not need equation-solving, and enable an automatic choice of parameter increment responding to the given interpolation tolerance in calculation of the character points of ellipse-arc. The algorithm also has advantage in approximation error control, which can control the approximation error to an expected one. Compared with present line-approximation mode, this algorithm, which needs no extra time and space in calculation, is applicable to CNC environment. The algorithm is specially valuable in cavity and contour machining.