Abstract: The finite element method for solving geometrical nonlinear boundary value problems (BVPs) of beam structures was first established upon the basis of Lagrange theory updated, and its correctness was verified here after by using the open literature data. To improve the computational efficiency of the commonly applied incremental iteration methods, the geometrical nonlinear BVPs were classified into two categories, i.e., BVPs with no-limit point and those with multi-limit point, according to the types of limit points, and the influence factors of the algorithm efficiency were analyzed simultaneously. An innovative combination method was developed by improving the prediction and correction strategy of the incremental iteration method, and its acceleration performance was quantitatively analyzed using three commonly-adopted examples, such as Lee Frame and so forth. Computational results indicate that the solution time of geometrical nonlinear BVPs of beam structures with no limit-point and 100,000 degrees of freedoms can be reduced to only 1/3 of the original algorithm, while the maximum relative error is less than 1%. The solution time of geometrical nonlinear BVPs involving multi limit-points can also be shortened to 2/3 of the original algorithm, and the maximum relative error is less than 1% as well. In future works, the combination methodology developed will be expected to be extended to geometrical nonlinear BVPs of continuum structures.