This paper addresses a dynamic model and a control method of a space robot with a rigid manipulator and a flexible appendage. The control method has been developed for performing multiple tasks: end-point motion control and vibration suppression control of a flexible appendage. A simple dynamic model that considers coupling between the manipulator and the flexible appendage is proposed for the control method. The tasks are performed simultaneously on the basis of their order of priorities using a redundant manipulator. Additionally, because vibration suppression requires feedback of the state of the flexible appendage, a state estimator of the appendage using a force/torque sensor is developed. Finally, the proposed model, control method, and state estimator were verified experimentally using an air-floating system.