Abstract: An algorithm to approximate offsets of ellipse curves by piecewise cubic Bézier segments is proposed.After some necessary partition,the offset curve of each elliptic arc is approximated by a cubic Bézier segment.And the n the whole offset curve with G¹ is obtained.On one hand,the algorithm is simple to calculate because the control points of the Bézier segment can be expressed explicitly.On the othe r hand,the global error estimation for the algorithm is given.The error estimation can be used to determine the number of the segments in the partition of the ellipse.