The inherent nonlinear hysteresis characteristics of giant magnetostrictive actuators are significantly influenced by the frequency of the input signal, and this rate-dependent effect poses severe challenges to high-precision modeling and control. To address this issue, this paper proposes an improved rate-dependent Prandtl–Ishlinskii (PI) model, which incorporates a rate-dependent envelope function with asymmetric left–right thresholds, and additional rate-dependent nonlinear terms to more accurately characterize the frequency-dependent hysteresis behavior of giant magnetostrictive actuators (GMAs). Based on this model, its inverse model is analytically constructed to achieve feedforward compensation, thereby substantially mitigating the influence of hysteresis nonlinearity. On this compensation basis, a sliding mode control strategy with prescribed performance is designed to guarantee global closed-loop stability, and to satisfy the predefined transient and steady-state performance on the tracking error. Finally, verification tests are conducted on a GMA experimental platform, and the results demonstrate that the proposed modeling and composite control scheme can effectively suppress rate-dependent hysteresis disturbances, achieving fast system response and desirable steady-state accuracy, thus validating the feasibility and engineering practicality of the method.