For a few decades, various methods to suppress the vibrations of structures have been proposed and exploited. These include passive methods using constrained layer damping (CLD) and active methods using smart materials. However, applying these methods to large structures may not be practical because of weight, material, and actuator constraints. The objective of the present study is to propose and exploit an effective method to suppress the vibration of a large and heavy beam structure with a minimum increase in mass or volume of material. Traditional tuned mass dampers (TMD) are very effective for attenuating structural vibrations; however, they often add substantial mass. Eddy current damping is relatively simple and has excellent performance but is force limited. The proposed method is to apply relatively light-weight TMD to attenuate the vibration of a large beam structure and increase its performance by applying eddy current damping to a TMD. The results show that the present method is simple but effective in suppressing the vibration of a large beam structure without a substantial weight increase.