Semi-analytical simulation (SAS) is a methodology that derives power series as an approximate solution in power system steady-state or dynamic analysis. Pade approximation is able to further improve the efficiency of SAS, while its computation for large-scale power systems is time-consuming. This letter proposes a vectorized fast algorithm for computing Pade approximation of a large-scale SAS. The Levinson algorithm is used to reduce the temporal and spatial complexities. Considering the structural homogeneity of computation, a vectorized version of Levinson algorithm is realized to achieve instruction-level parallelism. The novel approach is tested on the SAS of Polish 2383-bus system, which verifies the advantage of Levinson algorithm and vectorization in boosting the computation speed of SAS.