Abstract: As the present reaction null space planning for the incomplete kinematic properties of the space manipulator during the general operation involvesn either the impact of joint dead-zones on the system nor the relationship between the manipulator and the target to be grasped, it can not ensure the effectiveness of the tracking control in the presence of joint dead-zone. In this paper, the study of reaction null space planning and control in the final period before intercepting a target of a free-floating three-link space manipulator with joint dead-zone is focused. First, the dynamic model of a free-floating three-link space manipulator with joint dead-zone is established by the second Lagrange equation, in which the position and attitude of the carrier are uncontrolled. Then, the reaction null space mathematical model of the free-floating three-link space manipulator with joint dead-zone is derived, and the vector norm constraint algorithm of the reaction null space is studied. Furthermore, a nonsingular fast terminal sliding mode control algorithm with anti-interference and high convergence is proposed, in which it combines the double power reaching rate of variable coefficient with the nonsingular fast terminal sliding mode surface to improve the convergence speed and interference immunity. The dead-zone of the joint may reduce the control accuracy of the space robot system. In order to eliminate the influence of the free-floating three-link space manipulator’s joint dead-zone, an adaptive dead-zone compensator is designed. This compensator can approach the upper bound of dead-zone characteristics by self-adaptive control to eliminate the effect of the joint dead-zone on the system and to ensure the effectiveness of the tracking control. Finally, based on the Lyapunov function method the stability of the system is proved, and numerical simulation is carried out. The simulation results show the desired reactionless trajectories are tracked with the base’s attitude reactionless and the effectiveness of the proposed planning and control algorithm is demonstrated.