Abstract: In CAD, progressive iterative approximation (PIA) method has a wide range of applications for solving curve and surface approximation and fitting problems due to its good adaptability and stable convergence.In this paper, an efficient approximation method of the plane freeform offset curves based on PIA is proposed.Firstly, original data points are sampled on the offset curve.Secondly, parameterization is carried out on these points based on the Floater's method.By taking these sample points as original control points, an initial approximating curve is obtained.Then, by studying the errors between sample points and approximating points which have same parameter values, the PIA method is applied to minimize the corresponding errors.In our approach, the polynomial approximation method and rational approximation method are both considered in the offset approximation.Numerical examples show that our method has distinct advantages.