The deflector by controlling the warhead relative to the missile deflection of a certain angle to change the aerodynamic characteristics and trajectory characteristics of the projectile to achieve the control of the shooting point. Based on this background,a flexible hinge amplifier is designed to amplify the output displacement of the Giant Magnetostrictive Actuator（GMA）. First of all,the maximum output displacement of the amplification mechanism is deduced and calculated. Then,under the given displacement,it is calculated that there is a linear relationship between the input force and the output displacement. The existence of the linear relation is verified by the simulation of the finite element software,compared with the calculated results,it is concluded that the existence of internal reaction force causes additional displacement loss. Finally,combined with the control principle of GMA output force,the relationship between output displacement and GMA output force and total magnetization is deduced.