Abstract: An efficient precise time-step integration algorithm tosolve large-scale transient problems is presented. The Krylov subspacemethod, the Pad\'e approximations and the dimensional expanding method ofordinary excitations are applied to modify the original precise time-stepintegration algorithm in order to improve the computational efficiency. Theproblems of arbitrary complex excitations can also be solved. For a large-scale system,the efficiency of the algorithm would be influenced because the dimension ofsystem extended by the dimension expanding method becomes higher,especially, forthe complex excitations. The present algorithm can solve the large-scale systemwithout difficulty by using the decreasing dimension analysis of the Krylovsubspace method. The efficiency of the new algorithm can be improved byanalyzing the exponentional matrix in a subspace instead of the originallarge space. More computational cost can be saved by selecting the parameterN carefully.