The invention belongs to the technical field of building structure vibration attenuation, and particularly relates to a tuned mass damping device utilizing eddy current for providing damping. The tuned mass damping device comprises a conductor plate and a permanent magnet, and is characterized by also comprising a main shaft, a spring and an eccentric mass block, wherein the eccentric mass block is fixedly arranged on the main shaft, or a rotating bearing is arranged between the eccentric mass block and the main shaft, one end of the spring is connected with the eccentric mass block, the conductor plate is fixedly arranged at one side of the eccentric mass block in a direction vertical to an axle line of the main shaft, the permanent magnet is positioned between the conductor plate and the eccentric mass block and is fixedly arranged on the eccentric mass block, a gap is formed between the conductor plate and the permanent magnet, and the conductor plate, the permanent magnet, the main shaft, the spring and the eccentric mass block jointly form a group of eddy current tuned mass damping structures. The eccentric eddy current tuned mass damping device has the advantages that the structure is simple, the practicability is high, safety and reliability are realized, the cost performance is higher, the tuned mass damping device can be widely applied to structure vibration control of various high-rise and super high-rise buildings, drawn-up structures or long-span buildings, and the market application prospects are very wide.