Aiming at the space manipulator/dexterous hand system screwing bolts on-orbit, the dimension chain errors of the system are analyzed firstly. To correct position and pose errors caused by zero-gravity and on-orbit assembly of manipulator and simulated orbital replacable unit, especially to eliminate the random errors caused by the dexterous hand grabbing an electric tool, a visual servoing control strategy is proposed. In the proposed strategy, the position and posture of the electric tool are measured by global cameras after astronauts calibrating its exact operating position and posture, and the manipulator is introduced into visual servo control. A visual servoing controller is designed, and the convergence proof and stability analysis of the control algorithm are given. In on-orbit implementation of bolt-screwing task of the manipulator, the requirement of position and pose errors less than 3 mm/2° is achieved.