Exact optimal classical closed-open-loop control is not achievable For the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. In this study, a new numerical algorithm for the sub-optimal solution of the optimal closed-open-loop control is proposed based on the prediction of near-future earthquake excitation using the Taylor series method and the Kalman filtering technique. It is shown numerically that how the solution is related to the predicted earthquake acceleration values. Simulation results show that the proposed numerical algorithm are better than the closed-loop control and the instantaneous optimal control and proposed numerical solution will approach the exact optimal solution if the more distant future values of the earthquake excitation can be predicted more precisely. Effectiveness of the Kalman filtering technique is also confirmed by comparing the predicted and the observed time history of NS component of the 1940 El Centro earthquake. Copyright (C) 2001 John Wiley & Sons, Ltd.