Abstract: The trajectory tracking control for the coordinated motion of a free-floating space flexible manipulator with unknown parameters is developed. With the momentum conservation law, the Lagrange equation of the second kind is utilized to model the dynamic function of the space flexible manipulator incorporating the assumed mode method. In case of system parameters are unknown, a wavelet based fuzzy neural network control scheme is designed. The control scheme can control the base attitude and joint angle of manipulator to track desired trajectories in joint space simultaneously. It requires no prior knowledge about a dynamic model and system parameters, and saves the off-line training time because the network weights are adjusted through online learning. Simulation result demonstrates the validity and feasibility of the proposed control scheme.