Summary: Anti-interference motion control and elastic vibration synchronous suppression of base and joints for an elastic-base elastic-joint space robot with uncertainties are studied. On the basis of equivalent linear spring assumptions about the elastic base and joints, the dynamic equations of the space robot are established, then both singular perturbation slow and fast subsystems are deduced with the equivalent stiffness concept. The traditional parameter adaptive control law is improved by using \(\sigma\) modification, and is then combined with the robust anti-interference control. An improved singular perturbation adaptive robust anti-interference control scheme is proposed for the slow subsystem to track the rigid motion trajectories of the base’s attitude and links’ joints subject to uncertain parameters and bounded external disturbances. A high-gain linear state observer is employed to measure the fast higher-order states in real time, and an improved optimal control method is designed for the fast subsystem to synchronously suppress the elastic vibrations of the base and joints. Simulation result demonstrates the validity of the presented hybrid control scheme in anti-interference motion control and vibration suppression of the space robot.