Abstract: OR curve is polynomial and rational parametric plane curve whose offsets are rational.We here utilize the necessary and sufficient condition for properly parameterized plane curves to be offset-rational and the definite endpoint conditions,construct G1quadratic OR curve and G1cubic OR curve with a modulating factor、G1quartic OR curve、C2OR curve with transition point、C2OR curve.A given Bézier curve is subdivided several segments by inserting knots.An OR-spline curve which is an approximation for the Bézier curve is constructed according to the conditions of endpoints of each subdivision.The exact offset to ORspline curve can be generated directly by means of properly parameterization,which further can be regarded as an approximation for the Bézier curve.The errors between the Bézier curve and OR-spline is also estimated.