To solve the problems of multi-axis coupling and hysteresis in a three-degree-of-freedom tip–tilt–piston piezoelectric stage， a coupled hysteresis model was designed to simultaneously characterize the coupling effect between multiple piezoelectric actuators and their own hysteresis effect. Its inverse model was used for feedforward compensation to increase the positioning and trajectory tracking accuracies of the stage. First， the control system and kinematics model of the three-degree-of-freedom piezoelectric stage were developed， and the three-degree-of-freedom motion of the end-effector was transformed into the outputs of three piezoelectric actuators. Then， a coupled hysteresis model based on the Prandtl–Ishlinskii model was established， and the parameters of the model and its inverse model were identified. Finally， the effectiveness of the coupled hysteresis model was verified through open-loop inverse model feedforward compensation， and a compound control method combining inverse model feedforward and feedback was used for trajectory tracking control. The experimental results indicate that the inverse open-loop compensation reduced the maximum coupling displacements between the three piezoelectric actuators by >70%， confirming the effectiveness of the developed coupling hysteresis model. The maximum root mean square errors of the compound control method combined with closed-loop feedback for tracking the spatial trajectory are only 0.06 mrad and 0.42 μm， which are reduced by 72% and 87.5%， respectively， compared with those in the case where only closed-loop feedback was used， and the maximum error is reduced by at least 76%. The proposed coupled hysteresis model and its inverse compensation can eliminate the influence of coupling hysteresis in the stage， and significantly increase the positioning accuracy of the stage.