Abstract: When calculating control points, the classical progressive iterative approximation of surface interpolation requires the computation of the Kronecker product of two collocation matrices, which is computationally intensive. To reduce the overall computational complexity of the interpolation algorithm, the matrix collocation equation for solving the surface interpolation is decomposed into two relatively simpler sub-problems, proposing alternating iterative approximation methods for bi-cubic B-spline interpolation surfaces. First, based on the effective splitting of the collocation matrices, the corresponding iterative formats are constructed, and the two types of iterative formats are alternately executed to approximate the control points of the interpolation surface; then, three types of alternating progressive iterative approximation methods, namely Richardson, Jacobi, and Gauss-Seidel, are constructed, and it is theoretically proven that they converge to the control points of the bi-cubic B-spline interpolation surface. The results of the data interpolation examples show that the proposed method is superior to several other splitting-based iterative approximation methods in terms of convergence speed and computation time.