This study presents a synthesis method of a nonstationary optimal controller with a time-varying criterion function for reducing vibration of a time-varying object such as rope of elevator and crane. For time-varying object a stationary optimal control is little effective in reducing vibration. Hence, a nonstationary optimal control method with time-varying weightings on a control input and state values is applied to the time-varying object. As an illustration, the performance of reducing vibration with respect to the rope-sway problem on a high-rise building is examined through numerical calculation. Moreover, from the viewpoint of wave propagation, we propose a method of reducing vibration with wave-absorbing controller to remove the reflected waves. Finally, the performance of these nonstationary optimal and wave-absorbing controllers are compared with that of the stationary optimal controller for case that the structure is subjected to Kobe earthquake.