This paper discusses the stability control problem for assembled spacecraft of space?based manipulator and target satellite after capturing operation is completed. The dynamical model of the space?based manipulator system is derived by Lagrange formula, and based on the coupling momentum and impulse transfer during operation process of space?based manipulator to capture the target satellite, the mathematical models which are suitable for the design of control system for free?floating space?based manipulator to on?orbit capture floating satellite are established. Using the above mathematical model, a nonsingular terminal sliding mode control algorithm based on fuzzy neural network is proposed. The mentioned control algorithm needs neither to parameterize the dynamic equations of the system linearly, nor knows any system parameters. Due to the use of self?learning capability of neural network to modify control rules of fuzzy control and membership functions, the fuzzy neural network can reduce the number of fuzzy rules in the identification of system parameter, and it may be more adapted for practical application of space?based manipulator system to on?orbit capture. Eventually, a complete analysis on the stability and the performance are performed by using Lyapunov theory. The correctness and applicability of the control scheme are manifested by comparison of simulation and experimental results.