This paper proposes an active control type of momentum exchange impact damper (AMEID) and its application to reducing shock vibration of the floor. The floor is modeled as a one-degree-of-freedom system. The active component of AMEID is realized by using a linear motor. The controller design of AMEID is based on the LQR optimal control theory. The simulation results show that the performance of AMEID is not affected by the mass ratio. In addition, the performance of AMEID is compared with the conventional passive momentum exchange impact damper (PMEID), the active mass damper (AMD) and the conventional active control method in reducing the floor shock vibration. It is shown that the shock reduction performance obtained by AMEID is larger than that obtained by PMEID. The power consumption and the stroke of the actuator for AMEID are lower than those of AMD. Furthermore, the transmitted force obtained by AMEID is smaller than that of the conventional active control.