This paper fucuses on the issues of model error and mechanism input dead zone in a free-floating space manipulator system, a novel adaptive fuzzy neural network control scheme is proposed to realize the trajectory tracking of the space manipulator system. An adaptive fuzzy neural network controller is employed to compensate for the uncertainties in the system model and input dead zones, respectively. Verification of the proposed control algorithm’s stability is accomplished through Lyapunov stability theory. Finally, simulation results verify the efficacy of the proposed control algorithm. The presented fuzzy neural network controller ensures that position and velocity tracking errors of the space manipulator converge to a neighborhood around zero, even in cases there is an input dead zone.