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Novel electro-hydraulic servo valves (EHSVs) usually require their actuators output large stroke bi-directionally. To meet these requirements, a special stack giant magnetostrictive actuator amplified by flexure hinge (FASGMA) was designed, the displacement model of this actuator was established, and experiments were conducted to verify the model. Firstly, considering the ways to provide bias magnetic field in traditional GMA, a specific structure, with permanent magnets (PMs) and short GMM rods located iteratively, was designed, whose output was amplified by a bridge-type flexure hinge. Then, based on the structure, a strain model of SGMA was established, which can describe the strain distribution along the GMM rod. In addition, the amplification ratio and eigenfrequency of the flexure hinge were analyzed by basic theories of mechanics and finite element method. Meanwhile, with an optimization design method proposed, the structural parameters of the amplifier were decided. Moreover, a multi-DOF displacement model of FASGMA was set up, which considered the interaction of flexure hinge and SGMA as well as the strain distribution along the axial direction of SGMA. After that, the number of DOF was determined. Finally, an experimental system was established, and the proposed model was verified by both step and sinusoidal experiments. The results indicated that when the FASGMA was excited by step signals, the maximum output displacement was about 130μm, the response time was about 70ms. Under harmonic excitation, the frequency bandwidth was about 60Hz and the actuator performed a good tracking behavior with the excitation signal.