A vibration suppressing device and a vibration suppressing method that are capable of obtaining an accurate optimum rotation speed and shortening a time period from generation of chatter vibration to calculation of the optimum rotation speed are provided. The vibration suppressing device 10 includes: vibration sensors 2a to 2c for detecting time-domain vibrational accelerations of a rotary shaft 3 in rotation; and a control device 5 for calculating a chatter frequency and a frequency-domain vibrational acceleration of the rotary shaft 3 at the chatter frequency on the basis of the time-domain vibrational accelerations detected by the vibration sensors 2a to 2c, and when the calculated frequency-domain vibrational acceleration exceeds a predetermined threshold value, calculating an optimum rotation speed on the basis of a predetermined parameter, and rotating the rotary shaft 3 at the calculated optimum rotation speed.