Abstract: The control problem of coordinated motion of a free-floating space manipulator is discussed. Through the Lagrangian approach, the dynamic equation of the free-floating space manipulator was derived. Based on the above results, the free-floating space manipulator system was modeled by the RBF neural network technique, the GL matrix and its product operator. With all unknown inertial parameters, the adaptive neural network control scheme for coordinated motion between the base attitude and the end-effector of the free-floating space manipulator was developed. This proposed control scheme need neither linearly parameterize the dynamic equation of the system and know any actual inertial parameters, nor train and learn neural network offline. Thusly it is prone to a real-time and online application. A planar free-floating space manipulator with two links was simulated to verify the feasibility of the proposed control scheme.