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In this paper, optimal design of hybrid low damping base isolation and magnetorheological (MR) damper has been studied. Optimal hybrid base isolation system has been designed to minimize the maximum base drift of low damping base isolation system where for solving the optimization problem, genetic algorithm (GA) has been used. In design procedure the maximum acceleration of the structure has been limited, too. To determine the volatge of semi-active MR damper the H2/LQG and clipped-optimal control algorithm has been applied. For numerical simulations, a three-story frame equipped with the hybrid base isolation and MR damper subjected to the scaled El Centro excitation and optimal hybrid system has been designed. Results of numerical simulations have proven the effectiveness of the optimal hybrid control system in controlling the maximum base drift of isolated structure. Also comparing the performance of hybrid, low and high damping base isolation systems has shown that adding MR damper to low damping base isolation system has improved its performance so that the hybrid system has worked better th an high damping base isolation in reducing the maximum base drift. Testing optimal hybrid control system under different excitations has shown its efficiency.