In the FEM dynamic analysis of large flexible space structure (LFSS), thesolution of frequencies and corresponding models is actually a general eigenvalueand eigenvector problem. In this article, Lanczos method was applied to thistype of problem. In numerical examples, the convergency, accuracy-time relationand multi-root problem of Lanczos method for beam structure were analyzed.Considering the characteristic of the stiffness matrix of beam structure, the authoralso present some ideas to improve Lanczos method by iteration method.