Abstract: For stability control problem of tethered space robot for capturing uncontrolled target, a coordinated stability control method is proposed, which combines active damping control of space manipulator and attitude stability control of space base by using space tether and reaction wheel. Firstly, the dynamics model for capturing the target, contact and impact model between tethered space robot and target are established, and movement states of tethered space robot and the target are analyzed. Next, the active damping control law of space manipulator joint is introduced in order to reduce the impact force on the end of space manipulator. A sliding mode attitude control law is designed based on changing attitude of space base, and the control torque required by space base is supplied through space tether and reaction wheel. The proposed coordinated stability control method is analyzed and compared with the joint active damping control method in the simulation process of capturing the target, and the results show that the proposed method can keep space manipulator and space base stable, and the interferential influence of space tether on space base and target is tiny, which meets the stability requirements for capturing the target of tethered space robot.