A precision positioning stage based on giant magnetostrictive actuator (PPS-GMA) shows nonlinear displacement when it is used in the field of precision positioning control. To improve the defect, the Jiles–Atherton hysteresis model and the dynamic recurrent neural network (DRNN) feed forward-fuzzy PID feedback control strategy were adopted. An accurate hysteresis nonlinearity model of PPS-GMA was established with the Jiles–Atherton model and its parameters were identified using the particle swarm optimization (PSO) algorithm. A dynamics inverse model of the PPS-GMA was established with the DRNN learning method to compensate the hysteresis nonlinearity characteristic. A fuzzy PID feedback control was used to compensate for the mapping error of DRNN. Using these control methods, the positioning accuracy of the precision positioning stage was improved. The simulation and experimental results show that the Jiles–Atherton hysteresis model can describe the hysteresis nonlinear characteristic of the precision positioning stage, the PSO algorithm has high precision for parameter identification, the DRNN feed forward-fuzzy PID feedback control strategy can effectively eliminate the nonlinear characteristics of the PPS-GMA, which has practical significance for improving the positioning accuracy of the PPS-GMA.