Suppression of 1 degree of freedom flutter by gyroscopic damper is studied. The stability of the system equipped with the damper is examined using Routh's criterion, and the optimal design parameters are proposed. The comparison of the response of the gyroscopic damper with that of tuned mass damper reveals that the gyroscopic damper requires smaller added mass because of the effect of gyro-moment. The overall response of the system equipped with the damper is also presented from the view point of the responsive amplitude and frequency, which are important in practical design.