Piezoelectric micropositioning system (PMS) plays an important role in precision positioning applications. However, due to the inherent hysteresis nonlinearity of piezoelectric materials and the external disturbance of the system, these timevarying uncertainties seriously affect the positioning accuracy of piezoelectric materials. In response to the problems, an adaptive robust finitetime control strategy based on function approximation was proposed for PMS, the positioning accuracy of which was subjected to external disturbances, hysteresis and other timevarying nonlinear uncertainties. The trajectory tracking control law for PMS was designed by introducing a terminal sliding surface with continuous nonsingular and finitetime convergence characteristics. The dynamic approximation was carried out by using Fourier series, making the controller independent to the boundary information of the system’s uncertainties. A fuzzy logic system was then used to online compensate the approximation error. Finally, a Lyapunov function was applied to obtain the adaptive laws of Fourier coefficients and fuzzy adjustment parameters, and the finitetime stability of the proposed controller was proved. Simulations and experiments were carried out to verify the robustness and effectiveness of the proposed control strategy. In the simulations, the proposed control strategy was compared with the fast nonsingular terminal sliding mode control and the adaptive fuzzy sliding mode control based on function approximation, and the performance of the three controllers in tracking multi-frequency sinusoidal and triangular trajectories was tested. The robust antidisturbance ability of the controllers was also verified. The experimental results further showed the superiority of the proposed controller.