This paper addresses a time-optimal manipulator control strategy of a free-floating space robot with constraint on reaction torque induced by the manipulator motion. When a manipulator of a space robot is controlled, rotational motion of the base body is induced by the reaction torque. Assuming that reaction wheels are used to cancel the reaction and to stabilize the base attitude, the torque limitation of the wheels should be considered in order to realize zero base rotation of the robot. In this paper, a time-optimal control strategy of a free-floating space robot is discussed considering an arbitrary prescribed path for the manipulator hand and the dynamic constraints on reaction torque. The strategy is verified by numerical simulation with a free-floating space robot model equipped with a 7DOF (degrees-of-freedom) manipulator and a sytem of three reaction wheels.