Abstract: The dynamics modeling, algorithm design of motion control and step active suppression of joint-link double flexible vibration of free-floating flexible space robot are discussed. The system dynamic equations are established according to system momentum conservation, angular momentum conservation and Lagrange-assumed mode method. Based on singular perturbation method, the system is decomposed into a slow subsystem (represents the system's rigid motion), a fast subsystem 1 (represents the system's flexible motion caused by flexible-link), and a fast subsystem 2 (represents the system's flexible motion caused by flexible-joint). For the slow subsystem, a robust controller is proposed to compensate the uncertain parameters and rotation errors, and to realize the asymptotic tracking of the system's motion trajectory. For the fast subsystem 1, linear quadric regulator (LQR) is used to suppress the flexible vibration caused by flexible-link. For the fast subsystem 2, a feedback controller based on the velocity difference between the link and the motor is used to suppress the flexible vibration caused by flexible-joint. So the system's controller is a synthesize controller by the three controllers. The simulation results prove the controller's efficiency.