Abstract: By combining instantaneous optimal control and iterative learning control(ILC), one new hybrid control strategy called instantaneous optimal iterative learning control is proposed. Linear system is chosen as the model for the new control strategy, and the quadratic performance function of the system is chosen as the objective function to be minimized. During the process of controlling responses of the system, the core idea of the iterative learning control is introduced in order to modify the control signals. By introducing the norms of matrices, the sufficient condition of convergence for the new control strategy is established in the paper. The model of a 20-floor building in the second generation benchmark vibration control is selected for numerical simulation. In the numerical simulation, the north-south component of the El wave is introduced as the excitation. Comparing to the instantaneous optimal control, results of the simulation show that instantaneous optimal iterative learning control improves the effectiveness.