This paper addresses an inversion-free model predictive control with error compensation for piezoelectric actuators (PEAs), which is based on a dynamic linearized multi-layer feedforward neural network model. By the proposed method, the inverse model of the inherent hysteresis in PEAs is not required, and the control law can be obtained in an explicit form. By using the technique of constrained quadratic programming, the proposed method still works well when dealing with the plant physical constraints. Moreover, an error compensation term is introduced into the control law to attenuate the steady-state error. To verify the effectiveness of the proposed method, experiments are conducted on a commercial PEA. The experiment results show that the proposed method has a good tracking performance for PEAs.