For a piezoelectric tube scanner (PTS), this paper proposes an improved direct inverse tracking control algorithm and apply it to an atomic force microscope (AFM) to accomplish high-speed scanning tasks. That is, to enhance the high-speed tracking control performance of a PTS, an improved direct inverse rate-dependent Prandtl–Ishlinskii (P–I) model is firstly constructed, which includes a polynomial module to eliminate the structure nonlinearity. Based on the model, a practical feedforward control law is then designed to implement high-speed tracking control for a high-frequency trajectory with strong robustness, which presents the advantages of high-speed response, simple structure and convenient implementation. Subsequently, the designed feedforward law is combined with a feedback component, and the combined control strategy is employed in an AFM to accomplish fast imaging tasks. Numerous experimental results are then collected, which convincingly demonstrate the superior performance of the proposed practical model/control scheme.