The dual-motor drive pitch system is a strong coupling nonlinear time-varying system. The parameters of the two servo motors will also change during operation, resulting in inaccurate mechanism model of the system and affecting the synchronous control accuracy of the two motors. In this paper, a data-driven model based on improved sparrow search algorithm to optimize hybrid kernel extreme learning machine (CGSSA-HKELM) and a dual-motor model predictive synchronous control system based on quantum genetic algorithm (QGA) to solve the objective function are proposed. Firstly, the kernel extreme learning machine regression principle is used to establish a unified prediction model for two motors, which improves the accuracy, generalization ability and learning speed of the prediction model. Secondly, aiming at the problem that the kernel extreme learning machine is sensitive to parameter settings, the improved sparrow search algorithm is used to optimize its model parameters and conduct offline training to obtain a prediction model with adaptive ability. In the constructed model predictive synchronous control system, quantum genetic algorithm is introduced to optimize the objective function, so as to avoid falling into local optimum and obtain the optimal control of two motors. Finally, in order to prove the effectiveness of the scheme, simulation and experimental verification are carried out. The results show that the torque error of the two motors is reduced by 45% and the torque ripple is reduced by 40% compared with the cross-coupled sliding mode control strategy. The simulation and experimental results effectively prove the rationality and effectiveness of the dual-motor model predictive synchronous control scheme designed in this paper.