This article presents an incremental linear model predictive control (ILMPC) scheme based on the global linearization prediction neural network (GLPNN) model to compensate nondispersed and dispersed hysteresis. Hysteresis seriously weakens the tracking performance of piezoelectric actuators (PEAs), and the existing modeling and control methods mainly focus on the compensation of nondispersed hysteresis. This article investigates the GLPNN model of PEA to capture hysteresis behavior over a wide frequency band. The model is precisely identified by a specially designed neural network related to historical inputs, which is data driven. The modeling results verify that the modeling error is less than 10% of the previous models. Based on the identified model, linear control theory can be utilized for nonlinear hysteresis compensation. The real-time ILMPC scheme is proposed to achieve hysteresis compensation, which avoids complex nonlinear optimization problems. The experimental results indicate that the new compensator advances in eliminating hysteresis over a wide frequency band. Especially, the tracking error is significantly lower than previous studies in the dispersed band, and the relative hysteresis loop error is reduced by 55.24%. Different from the existing compensation strategies for limited bandwidth, the proposed modeling and control methods exhibit better tracking performance for PEAs over a wide nonresonant frequency band.