The offshore environment is complex and volatile, and the combined wind and wave loads can generate large vibrations on the floating wind turbine platform and tower top, posing a serious threat to the structural safety of the wind turbine system. To cope with this challenge, a tuned mass damper (TMD) was installed in the nacelle of the barge floating wind turbine to form a hybrid mass damper (HMD) using active driving force. The H∞ algorithm was used for the drive force control. The effects of no control, passive control, and H∞ control were compared through simulation. The results show that the H∞ control can effectively reduce the longitudinal angle of the platform and the longitudinal displacement of the top of the tower, with obvious vibration suppression effects.