Considering the control problems caused by uncertainties such as inaccurate modeling, external disturbance and joint flexibility, a neural network control method based on H∞ is proposed. By establishing the dynamic model of the free-floating space robot with flexible joints, according to its dynamic characteristics, it is split into a slow subsystem model representing the rigid characteristics and a fast subsystem model representing the flexible characteristics. Based on the H∞ robust control theory, a robust controller based on neural network is designed to realize the decoupling control of the rigid dynamic model, The designed weight adaptive learning rate can ensure the online and real-time adjustment of parameters. Based on Lyapunov theory, it is proved that the designed controller can ensure that the L2 gain of the system is less than the given index. A feedback controller based on velocity differential is designed to compensate the angle error caused by joint flexibility. The experimental simulation results verify that the proposed control method is effective and has good engineering application value.