A new controller is proposed for a dual motor servo system with nonlinear dead zone. The proposed controller consists of a tracking controller and a synchronization controller. The tracking controller combines the predetermined performance function (PPF) and the state predictor into the neural dynamic surface, so as to ensure the transient and steady state responses within the preset boundary of the tracking error. Different from the traditional adaptive control method, the proposed control method updates the neural network weight by predicting the error, which can quickly and smoothly approximate the nonlinear disturbance without causing high-frequency vibration. In addition, an optimal sliding mode synchronization controller based on the average deviation coupling strategy is proposed to solve the coupling problem between synchronization and tracking. Finally, the effectiveness of the design method is verified by simulation.