According to the requirements of actuators for novel electro-hydraulic servo valves (EHSVs), this paper proposes a design for a special stack giant magnetostrictive actuator (SGMA). In order to compensate for the nonlinear property of the SGMA, a controlling strategy was proposed and verified by simulation and experimentation. First, with permanent magnets (PMs) and short giant magnetostrictive material (GMM) rods located iteratively, a highly uniform bias magnetic field was obtained in the SGMA. Then, based on the structure of the SGMA, a multi-DOF model was established to describe the dynamic properties of this actuator. In addition, a control methodology was developed, which combines model predictive control and sliding mode control. Finally, to validate the proposed controller, both simulation and experimentation are conducted, and the results indicate that the proposed controller can realize the ultra-precise control of the SGMA. In the step control experiment, the system achieves stability within 1.5 ms with no overshoot or steady-state error. In the sinusoidal control experiment, the maximum tracking error of the system is approximately 0.83 μm, 6.9% of the total output of the SGMA, proving that the model predictive sliding mode control can significantly reduce the nonlinearity of the SGMA.