Unstable vibration occurs in the vicinities of the major critical speeds of asymmetrical shaft and rotor systems. It occurs also in a wide rotational speed range higher than the major critical speed of a shaft with a hollow disk partially filled with liquid. The occurrence of the unstable vibrations is a serious problem because the amplitude increases exponentially, and finally, the system is destroyed. The active vibration control can suppress unstable vibrations but the method is generally complicated and costly. No simple effective method to suppress unstable vibrations has been developed yet. In the previous paper, the authors proposed a simple method by utilizing discontinuous spring characteristics, which can suppress steady-state resonances. This paper shows that this method is also effective to suppress unstable vibrations. By using this method, the unstable vibrations can be changed into almost periodic motions, and the amplitudes are suppressed to the desired small level even in an unstable range. The validity of the proposed method is also verified by experiments.