Aiming at the design change problem caused by unexpected events for production and supply chain system, a data-driven predictive control algorithm was designed to meet the uncertain the customers' demands. Firstly, the production and supply chain system was modeled as a multi-agent system according to the collaboration relationship among the agents. Secondly, a distributed model-free adaptive predictive control algorithm was designed to enable the production inventory level in the supply chain system to meet the customers' demands. Thirdly, by introducing the input and output data of future moments, the algorithm design for product and supply chain system can predict the inventory level in the future period. Finally, the convergence of the algorithm was analyzed and effectiveness of the proposed algorithm was verified by numerical simulation. The results show that the propose method can effectively control the productivity of the system, so that the production inventory level after change meets the market demand.