Abstract: Offset curves has been widely used in CNC (computer numerical control) machining process,robot walking route etc.,comparing with the original curve,offset curves are more complex,and can't be represented by rational curve except for special cases. In order to be compatible with existing CAD/CAM system,based on the Bézier polynomial approximation of circular arcs,a new algorithm is proposed to approximate offset curves of Bézier curves. At first,by use of Tchebyshev polynomial to approximate circular arcs,we present an arbitrary order Bézier polynomial approximation of circle,then use it to derive the approximation for offsets of Bézier curves,which is a new Bézier curve with the same degree of the base curve. Two examples are given finally for comparing with other methods,the results show that the effectiveness of our method similar to other methods,but our method reduces the approximation degree.