Abstract: For the problem of trajectory tracking control of free-floating space robot in inertial space, the existing solutions just achieve asymptotical stability, and the transient performance of the system isn't analyzed. To solve this problem, a kind of adaptive backstepping neural network control law based on error transformation is proposed. The constrained outputs are transformed into unconstrained control variables, and then an adaptive backstepping neural network control law is designed to realize unconstrained variable stable control with uncertain dynamic and kinematic parameters. The proposed control algorithm can not only guarantee the globally asymptotical convergence of the trajectory tracking errors in task space, it can also provide additional ensure for the prescribed transient tracking performance of the closed-loop system. The system tracking performance is improved significantly. Finally, numerical simulation is conducted to prove the feasibility and effectiveness of the proposed control strategy.