Abstract: Progressive-iterative approximation(PIA)is an efficient method for data fitting that attracts the attention of many researchers and has a wide range of applications.However,the convergence rate of LSPIA is prolonged.In this study,we design a fast PIA format based on the Gauss-Seidel iterative method named Gauss-Seidel progressive and iterative approximation for least squares curve and surface fitting(GS-LSPIA).Firstly,the control points of the fitting curve(surface)are selected from the given data points.Then,the chord length method is used to assign the parameters of the given data points.GS-LSPIA generates a series of fitting curves(surfaces)by refining the control points iteratively,and the limit of the generated curve(surface)is the least square fitting result to the given data points.Several experimental results presented in this paper demonstrate that,to achieve the same accuracy for GS-LSPIA and LSPIA,GS-LSPIA required fewer steps and shorter running time compared with LSPIA.Thus,the proposed GS-LSPIA is efficient and has a faster convergence rate compared with the LSPIA algorithm.