A tunable mass damping device, including a connecting, a weighted assembly, and a top connecting assembly connecting an upper end of the connecting rod with a tower beam of a tower and including an anti-rotation mechanism. The anti-rotation mechanism includes: a laterally extending fixing plate fixedly connected with the tower beam through a longitudinally extending supporting member; a laterally extending first movable plate arranged under the fixing plate and fixedly connected with the upper end of the connecting rod; and two connecting shafts spaced apart from each other. Each of the connecting shafts has a lower end fixedly connected to the first movable plate, and an upper end inserted into the fixing plate and connected therewith through a connecting head. The connecting head includes an intermediate elastic layer arranged between inner and outer sleeves of the connecting head.