This paper discusses a vibration suppression control method for a space robot with a rigid manipulator and flexible appendage. A suitable dynamic model that considers the coupling between the manipulator and flexible appendage was developed for the controller to accomplish the vibration suppression control of the flexible appendage. The flexible appendage was modeled using a virtual joint model, and the control method was developed on the basis of this model. Although this type of control requires feedback of the flexible appendage state, its direct measurement is generally difficult. Thus, an estimator of the flexible appendage state was constructed using a force/torque sensor attached between the base and flexible appendage. The control method was experimentally verified using an air-floating system.