Based on the fuzzy logic of the Takagi-Sugeno (T-S) model and the bang-bang control law, a fuzzy sub-optimal bang-bang control method is presented in this paper. Genetic algorithm is used to determine the optimal control force in the T-S model. The relative performance index is utilized as the objective function. A building structure with a semi-active friction damper is applied as numerical example, and its seismic reduction effectiveness and adaptability are investigated. The results indicate that the proposed control strategy not only effectively suppresses the structural vibration but also is adaptive to varying excitations from weak to strong earthquakes.