A tunable mass damping device, comprising: a connecting rod extending in a longitudinal direction; a weighted assembly connected at a lower end of the connecting rod; and a top connecting assembly, which is connected between an upper end of the connecting rod and a tower beam for a tower, and includes an anti-rotation mechanism, the anti-rotation mechanism comprising: a laterally extending fixing plate, which is fixedly connected to the tower beam through a longitudinally extending support member; a laterally extending first movable plate, which is 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, wherein each of said connecting shafts extends in the longitudinal direction, and 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, wherein the connecting head includes an outer sleeve connected to the fixing plate, an inner sleeve arranged in the outer sleeve and connected to a respective one of the connecting shafts, and an intermediate elastic layer arranged between the inner sleeve and the outer sleeve. a connecting rod extending in a longitudinal direction; a weighted assembly connected at a lower end of the connecting rod; and a top connecting assembly, which is connected between an upper end of the connecting rod and a tower beam for a tower, and includes an anti-rotation mechanism, the anti-rotation mechanism comprising: a laterally extending fixing plate, which is fixedly connected to the tower beam through a longitudinally extending support member; a laterally extending first movable plate, which is 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, wherein each of said connecting shafts extends in the longitudinal direction, and 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, wherein the connecting head includes an outer sleeve connected to the fixing plate, an inner sleeve arranged in the outer sleeve and connected to a respective one of the connecting shafts, and an intermediate elastic layer arranged between the inner sleeve and the outer sleeve. a laterally extending fixing plate, which is fixedly connected to the tower beam through a longitudinally extending support member; a laterally extending first movable plate, which is 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, wherein each of said connecting shafts extends in the longitudinal direction, and 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, wherein the connecting head includes an outer sleeve connected to the fixing plate, an inner sleeve arranged in the outer sleeve and connected to a respective one of the connecting shafts, and an intermediate elastic layer arranged between the inner sleeve and the outer sleeve.