An isolation system is not very effective when an inappropriate level of damping is used. This paper proposes a theoretical method which can be used to determine the optimal frictional coefficient of an isolation system. Only a one-dimensional isolation system and ground motion are considered. The frictional coefficient is optimized by minimizing the sum of squares of structural absolute accelerations, with the optimization results being validated graphically. Sensitivity studies were used to verify the feasibility of the optimal frictional coefficient, coupled with a practical example in Taipei under the conditions of the Hualien and El Centro earthquakes. Consequently, the feasibility and reliability of the proposed optimal design were verified.