A tremor which is one of the involuntary motions is somewhat rhythmic motion that may occur in various body parts. Although there are several kinds of the tremor, an essential tremor is the most common tremor disorder of the arm. The essential tremor is a disorder of unknown cause, and it is common in the elderly. The essential tremor interferes with a patient's daily living activity, because it may occur during a voluntary motion. If a patient of an essential tremor uses an EMG-based controlled power-assist robot, the robot might misunderstand the user's motion intention because of the effect of the essential tremor. In that case, upper-limb power-assist robots must carry out tremor suppression as well as power-assist, since a person performs various precise tasks with certain tools by the upper-limb in daily living. Therefore, it is important to suppress the tremor at the hand and grasped tool. However, in the case of the tremor suppression control method which suppressed the vibrations of the hand and the tip of the tool, vibration of other part such as elbow might occur. In this paper, the tremor suppression control method for upper-limb power-assist robot is proposed. In the proposed method, the vibration of the elbow is suppressed in addition to the hand and the tip of the tool. The validity of the proposed method was verified by the experiments.