This paper studies the free- oating space robot as a control object. In order to answer the question how control precisions are ensured after a great quality target is caught by a space robot arm, this paper brings forward a robust control method based on neural networks. Because of the in uence of such factors as measuring errors and outside disturbance, two kinds of uncertainties exist in the space robot system, namely, parameter uncertainties and the non- parameter uncertainties. The radial function neural network makes use of the study ability of itself. Parameter uncertainties are studied by the neural network, and the network weights between concealed layer and output layer are adjusted online real-time. Non-parameter uncertainties and approach errors are compensated by the robust controller, and two controllers are integrated by redundancy theory. Global asymptotic stability of the whole closed-loop system based on Lyapunov theory is demonstrated in the paper. This scheme does not need a precise space robot model. Simulation results show that the controller is valid. The space robot manipulators run at the low speed condition, which provides ample study time for the neural network, so engineering application real-time quality is guaranteed because of the above reasons. The control method brought forward by this paper has potential applications in defense, aerospace and other major security fields.