This paper proposes a new training algorithm using a hybrid Jaya-back propagation algorithm (called H-Jaya) to optimize the neural network weights, which is applied to identify the nonlinear hysteresis Piezoelectric actuator based on the experimental input-output data. The identified H-Jaya-neural model will be used to design an advanced feed-forward (FF) controller for compensating the hysteresis nonlinearity. Furthermore as to improve the tracking performance, a feed-forward-feedback control scheme is conducted. To evaluate the effectiveness of the proposed approach, firstly, it is tested through identifying the nonlinear hysteresis of Piezoelectric (PZT) actuator and compared with other meta-heuristic techniques, including differential evolution (DE), particle swarm optimization (PSO), and Jaya. Then, the accuracy of the hysteresis model-based compensator is evaluated under various control experiments using the piezoelectric actuator. The results of experiments executed on PZT actuator configured with a PZS001 from Thorlabs prove that the proposed approach obtains an excellent performance in hysteresis modeling and compensation.