One of the challenges in civil engineering is to find innovative and better means of suppressing structural vibration due to earthquakes and wind gusts. This paper proposes a new semi-active control strategy of variable friction dampers, such as a piezoceramic friction damper, based on an improved suboptimal bang-bang control algorithm that is modified by a continuous function of story velocities. By using genetic algorithm, the amplitude of the control force and preloading friction in the control system are obtained to enhance the seismic performance of controlled structures. The approach presented here is applied to a three-story building with a variable friction damper installed in the first story. Numerical results demonstrate that the peak accelerations under seismic excitations have been greatly reduced and the proposed method has achieved a better adaptability than that of the unmodified controller