A structure vibration control device includes a hydraulic damper having damping force characteristics that vary in response to a magnitude of an earthquake and having characteristics that are maintained for a long period of time regardless of an environmental temperature change. The hydraulic damper includes a preload chamber into which a high-pressure gas is charged in series with a hydraulic chamber. The preload chamber absorbs a volume change of the hydraulic chamber caused by the environmental temperature change and a piston rod and balances a bias force of a spring within the hydraulic chamber and of the preload chamber. Piston valves have high damping force characteristics against a weak earthquake and low damping force characteristics against a strong earthquake. The piston valves may include an orifice beside a check valve function, by which the high damping force characteristics lie within a range of 150 to 800 kN/(m/sec).