This paper proposes a Linear Quadratic Guassian Design (LQG) with based semi-active control algorithm for vibration reduction of building structures. The controlled damper force required by the structure has been calculated from an MR damper of load capacity 100N. A building frame has been selected to illustrate the performance of the proposed algorithm. Four different earthquake acceleration data has been used as input vibration data to the numerical frame. The proposed method of damping on the frame has been found to be more effective to reduce the structural response significantly in comparison with the conventional tuned liquid column damper. The developed method is efficient in providing the optimum control force required to the frame. Therefore, it minimizes the need of high damping capacity and the number of dampers. As a result, it reduces the cost of maintenance and structural control during earthquakes.