An innovative method of wave-absorbing control is presented for vibration suppression of flexible space structures. The method needs no digital computation process programmed under the control law that is usually necessary in realistic systems. A torque motor is used not only as an actuator but also a sensor that detects the angular velocity of the motor shaft, and the control loop is closed without digital computation. The control approach is to treat the vibration as superposed wave modes traveling in positive and negative directions and to suppress the outgoing wave modes at the actuator position. The performance of the present method is verified through both numerical simulation and experiments.