This paper deals with a free-flying space robot which grapples a target satellite based on a visual feedback control scheme. As the robot body is not fixed in an inertial space, manipulator motion causes changes in the view of the visual sensor. Therefore the closed loop system for the manipulator controller involves the visual data processing which normally takes long calculation time. We construct a control system which is not explicitly affected by the calculation time and analyze stability of the system. Analysis results show that a stable control system can be constructed in spite of the long calculation time, on condition that the manipulator trajectory which is not close to singular points is settled. Moreover we developed a zero gravity motion simulator which combined a computer simulation and servo mechanisms. An experimental space robot system is constructed and experiments to grapple a target are performed on the simulator. It is confirmed through the experiments that the free-flying space robot automatically grapples the target with the visual feedback control scheme proposed.