The vibration suppression on a resonant system, based on the reflected wave rejection, has been recently proposed. In the method, the resonant system is modeled through a wave equation, in order to consider high order vibrations and vibration suppression is achieved by eliminating a reflected wave. However, it is difficult to implement such method when there are input and output time-delays, because it requires the implementation of the inverse of a time delay. Under such background, vibration suppression on the integrated resonant and time-delay system by using a modified reflected wave rejection has been proposed. However, a problem still remains, which is to need to use load-position information. Therefore, this paper proposes a novel vibration suppression method for systems including time delays by using a reaction-torque-based reflected wave rejection, which does not use the load position information. The novel reflected wave rejection can estimate and compensate the reflected wave by using motor position and reaction-torque information which is estimated by a reaction-torque observer. The validity of the proposed method is confirmed by experimental results.