In this study, the vibration mitigation of the structures under the earthquake excitation using magneto-rheological (MR) damper is researched. For this purpose, one MR damper is installed to an eight story structure and the system performance is investigated. MR damper is installed between the second floor and the ground. The MR damper is a semi-active control device that can be controlled by only the voltage transmitted to the electromagnetic coils. Since the MR damper is a semi active device, damping force can be changed by applied voltage. Therefore, determination of the applied voltage is important for vibration reduction. A robust controller is designed for determination of the MR damper voltage. H∞ method and model reduction approach are used for robust control design and application. The performance of the proposed method is tested by numerical simulation on the semi active structural system with MR damper. The performance of the control algorithm and the effect of the MR damper arrangement is evaluated using earthquake (El-centro earthquake) data. The results are compared with situations in which MR damper is not connected and when the MR damper is situation of semi-active controlled. The evaluations are based on the displacement and acceleration responses. The simulation results showed that the arrangement of the MR damper connected between the second floor and the ground is effective in reducing the vibration amplitudes.