Abstract This paper focuses on the fast and accurate offset method of high degree rational Bezier/NURBS curves. Firstly, in order to solve the scaling problem of the subdivision error in the Bezier/NURBS curve offsetting, a novel dynamic offset error control method which is the extension of the fast subdivision method of Bezier curve, and can realize the fast offset of the Bezier/NURBS curves under the user's required offset accuracy is proposed. Secondly, for the interpolation of the offset points, the local interpolation is adopted, which can effectively solve the problem of the mass calculation caused by the re-segmentation of the original curve when the interpolation accuracy check fails. Finally, the paper validates the efficiency of the proposed method by comparing the offset accuracy of a series of Bezier/NURBS curves with those of other methods.