Abstract: Classical progressive iterative approximation method is simple,intuitive,and effective for data fit-ting,but it is not enough to process mass data.The least square progressive iterative approximation(LSPIA)could make up for the limited data,and be suitable for fitting mass data.To improve the convergence rate of LSPIA,the Schulz iteration of Moore-Penrose generalized inverse is combined with LSPIA iterative format.The improved least square progressive iteration approximation format is proposed for triangular B-B sur-faces.And the iterative surface sequence converges to the least square fitting result to the given data points in second-order for 2,3,4-degree triangular B-B surfaces.Furthermore,the weight is calculated with the fastest convergence rate,and some numerical examples are presented to validate the correctness and effi-ciency of the improved LSPIA method.