This paper investigates the fixed-time control issue for the post-capture space tethered robot system in the presence of uncertainty and external disturbances. A new form of fixed-time nonsingular terminal sliding mode surface (FNTSMS) is constructed by introducing the power function to traditional terminal sliding mode surface (TSM), thus the system fast response and singularity circumvention are ensured gracefully. With the aid of FNTSMS, a new fixed-time control scheme is proposed for post-capture space tethered robot, which can achieve the high-precision tracking performance and fast response rate after the space targets are captured. Moreover, the proposed scheme is compared with the traditional boundary layer sliding mode control method. The simulation results verify the effectiveness of the proposed control scheme.