This paper investigates a neural network adaptive controller design method for turbo‐generator of power systems with external disturbance, unknown system dynamic, prescribed performance, and unknown actuator dead zone. First, the unknown system dynamic is estimated and overcome through a neural network. Using the implicit function theorem, the unknown asymmetric dead‐zone behavior of the actuator is overcome by another static neural network. Second, the external disturbance and the reconstruction error of neural networks are handled by a robust term updated online. Moreover, there is no requirement to pre‐know or off‐line estimate the reconstruction error of neural networks and the upper bound of the system external disturbance. Third, based on Lyapunov theory, the smooth control law is proposed. In the meantime, the uniform ultimate boundedness of the networks weights is strictly proved. Furthermore, the system state error satisfies the prescribed transient performance and can converge to a small neighborhood around zero. Finally, a numerical simulation shows the effectiveness of the proposed method.