There exist two problems: 1) the model uncertainties caused by flexible cable and 2) the oscillations caused by the asynchronous adjustment of multiple cable lengths, which make it difficult to achieve accurate tracking control of the end-effector (EE) for cable-driven parallel robots (CDPRs) in practical applications. This paper addresses a non-singular terminal sliding mode control scheme with the relative-coupling synchronization in the cable space (NTSM-RSC) to overcome the effect of the model uncertainties and suppress the oscillations of cables simultaneously. A non-singular terminal sliding mode controller (NTSMC) is proposed to enhance the robustness of the system to model uncertainties. A relative-coupling error vector of multiple cable lengths is established based on ring topology, and a relative-coupling synchronization controller in the cable space (RSC) is proposed to improve the synchronization of multiple cable lengths. The RSC is added to the NTSMC to improve the synchronization of cables compared with the NTSMC, namely the NTSM-RSC. The finite-time convergence of the error of system is theoretically guaranteed. The effectiveness and superiority of the NTSM-RSC are verified by experiments.