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Geometric iterative methods, including progressive iterative approximation and geometric interpolation methods, are efficient for fitting a given data set. With the development of big data technology, the number of fitting data points has become massive, and the progressive iterative approximation for least-squares fitting (LSPIA) is generally applied to fit mass data. Combining the Schulz iterative method for calculating the Moore–Penrose generalized inverse matrix with the traditional LSPIA method, this paper presents an accelerated LSPIA method for tensor product surfaces and shows that the corresponding iterative surface sequence converged to the least-squares fitting surface of the given data set. The iterative format is that of a non-stationary iterative method, and the convergence rate increased rapidly as the iteration number increased. Some numerical examples are provided to illustrate that the proposed method has a faster convergence rate.