To study the impacts of private information leakage on co-opetition relationships in a data-driven closed-loop supply chain in the Big Data era, firstly, we analyzed the importance of a Data Company in a supply chain in the new background. Then, we analyzed and built a new structure of the closed-loop supply chain with one central enterprise, one retailer, one Data Company, one third-party logistics and some scattered remanufacturers. Next, we considered private information leakage, and three new competition models of the closed-loop supply chain were constructed. Then, the optimal profit, optimal price, and competitive advantages of different competitors in the three new models were analyzed and compared. Findings: in the Big Data environment, the acquisition cost of private information, the logistics cost and the wholesale price affect the co-opetition relationship of the data-driven closed-loop supply chain. The acquisition cost decides who will win the competition. Finally, conclusions were verified by a numerical model.