A thixotropic material is charged in a container. The container also holds a movable member which is placed in the thixotropic material so as to stir the thixotropic material. A force transmitting element is connected to the movable member. When an object, the vibration of which is to be controlled, is out of resonance, the amplitude of vibration is so small that the thixotropic material is in a gel state, thus presenting a comparatively large spring constant for the vibration control apparatus. As the excitation frequency is increased towards the resonance range, the amplitude of vibration is increased correspondingly, so that the movable member stirs the thixotropic material to generate stress in the latter, whereby the phase of the thixotropic material is changed from gel to sol. Consequently, the natural frequency of the vibration system, including the object and the vibration control apparatus, is lowered, thus averting resonance. It is thus possible to obtain vibration restraining or control effect over a wide range of excitation frequencies.