Abstract: An extreme value condition is derived for optimal control to time-domain response of structures subjected to earthquake excitation by taking the special properties of structural vibration control into account. For the purpose of calculating the control force of a forced vibration system using LQR method, the extreme value condition presented in the study is conceptually rigorous. Several current algorithms for optimal control to structural vibration were compared, and the main improvement over the current algorithms was highlighted. A new algorithm of optimal control to structural vibration has been realized by using state transition method which is based on the similarity between the companion equation and the state equation. Three isolated buildings designed by the author are employed as numerical examples, and several important features such as the model expression and control effect of different algorithms are investigated due to three different earthquake signals.