In this paper, a new hybrid fault-tolerant control (FTC) strategy based on nonsingular fast integral-type terminal sliding mode (NFITSM) and time delay estimation (TDE) is proposed for a Schönflies parallel manipulator. In order to detect, isolate, and accommodate actuator faults, TDE is used as an online fault estimation algorithm. Stability analysis of the closed-loop system is performed using Lyapunov theory. The proposed controller performance is compared with conventional sliding mode and feedback linearization control methods. The obtained results reveal the superiority of the proposed FTC based on TDE and NFITSM.