Peak response is a more suitable index than mean response in the light of structural safety. In this study, a controller optimization method is proposed to restrict peak responses of building structures subject to earthquake excitations, which are modeled as partially stationary stochastic process. The constraints are given with specified failure probabilities of peak responses. LQR is chosen to assure stability in numerical process of optimization. Optimization problem is formulated with weightings on controlled outputs as design variables and gradients of objective and constraint functions are derived. Full state feedback controllers designed by the proposed method satisfy various design objectives and output feedback controllers using LQG also yield similar results without significant performance deterioration.