To suppress the torsional vibration caused by the omission of couplings and dampers during flexible power transmission in the permanent magnet (PM) synchronous drive system of pure electric vehicles (EVs), this paper presents a non-singular fast terminal sliding mode control (NFTSMC) torsional vibration suppression strategy based on a sliding mode disturbance observer (SMDO). First, a PM synchronous drive system is simplified as a two-inertia model, and a mathematical model is established. Then, an NFTSMC controller of the load-side speed feedback is designed to suppress torsional vibration. Meanwhile, an SMDO is designed to estimate the load disturbance, and the estimated value is fed back to the controller to perform feedforward compensation. The robustness of the system is improved, and the effect of the load disturbance on the system is reduced. The results of the simulations and experiments show that the presented NFTSMC based on the SMDO strategy has a strong torsional vibration suppression effect compared to PI control and conventional sliding mode control.