Abstract: Because the convolution curve of two compatible conics can not always be represented by rational curves,a new method for approximating the convolution curve is presented,which is called biarc approximation method.Firstly,approximate the two given compatible conics by biarc curves,and then,take the convolution curve of the biarc curves as the approximate curve.This method can not only make the approximate curve represented by rational quadratic Bézier curves,but also obtain the upper bound of the error in advance.Numerical examples show that the method in this paper is much effective in CNC machining and CNC drawing.