This paper proposes a novel vibration control of a resonant system by using a reflected wave rejection with a fractional order low-pass filter. In a conventional research, a vibration control using a reflected wave rejection based on wave equation was proposed. From the viewpoint of the wave, vibrations are suppressed by eliminating a reflected wave. The conventional method can suppress the all resonances by using a reflected wave rejection. However, the conventional reflected wave rejection assumes that poles of the resonant system are located on the imaginary axis at regular intervals. Considering real industry application, there is few case that the above assumption is realized. Therefore, in this paper, the resonant system is modeled as a wave equation including not only spring but also damper. Considering the damper effect, the proposed method is not restricted by the above assumption. In addition, based on the wave equation including the damper effect, this paper presents the method of eliminating the reflected wave. The reflected wave is eliminated by a novel reflected wave rejection with a fractional order low-pass filter. Finally, the validity of the proposed method is verified by simulation and experimental results.