When rotating machinery is operated above the major critical speed, self-excited vibrations appear due to internal friction of the shaft. Internal frictions are classified into hysteretic damping due to the friction in the shaft material and structural damping due to the dry friction between the shaft and the mounted elements. In this paper, a method to suppress the self-excited vibration using leaf springs are proposed. The structural damping is considered as the internal damping. The characteristics of a rotor with leaf springs are investigated systematically by using simulative and theoretical analyses. The validity of the proposed method is also proved by experiments.