We discuss a new type of space robot system composed of a spacecraft and a robot attached through a tether to it. The tethered robot is translated away from the spacecraft wing existing tether tension control techniques in gravitational field. Link motion of the tethered robot, however, is complicated, since the momentum is not constant due to the presence of external forces. This paper especially focuses on momentum control of the tethered robot. In addition to translational momentum control, we show that angular momentum of the tethered robot can be controlled by proper motion of the tether attachment point. We propose a control law for link motion of the tethered robot composed of two subtasks: The end-effector motion subtask and the tether attachment point motion subtask.