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Piezoelectric actuators (PZTs) are essential elements in high-precision systems. However, the hysteresis nonlinearity introduced by PZTs degrades the control accuracy. In this paper, a high-order terminal sliding mode enhanced hysteresis observer is designed, which compensates the error between the Bouc-Wen model and the actual hysteresis. Subsequently, a novel terminal sliding mode control (TSMC) is proposed. Unlike the conventional TSMC, the novel TSMC method makes the tracking error in the sliding mode converge to the origin within a finite time regardless of the initial conditions, which improves the performance of conventional TSMC. The stability of the proposed control method is verified through the Lyapunov theory. Finally, simulations and experiments are implemented to validate the effectiveness of the proposed control method. Experimental results demonstrate that the proposed method has a more superior performance than conventional TSMC.