Due to the increasingly serious energy crisis and environmental pollution, new energy vehicle (NEV) as a environmentally-friendly travel tool has been vigorously developed by various countries. However, in 2020, China officially enters the “postsubsidy era” in which the carbon trading scheme will replace the current fiscal and taxation system, affecting the implementation of NEV. Under the carbon trading policy, it has gradually become a major issue how NEV companies achieve production revenue coordination and carbon emission optimization decisions. This study focuses on building a multilevel supply chain for NEV production, sales, and component recycling. In addition, this study establishes a Stackelberg game model dominated by NEV manufacturers and uses contracts to coordinate the model. Results are as follows: (1) With the increasing maturity and perfection of enterprises’ carbon emission reduction technology, consumers’ demand for new energy vehicles will increase, and the effect will be more obvious when the system centralized decision-making. (2) Since the centralized decision is aimed at the total profit of the system and has the advantage of optimal order quantity, the total benefit of the supply chain is higher than that of the decentralized decision. Moreover, if the cost coefficient of carbon emission reduction is small, the total benefit of the supply chain under the centralized decision will be more obvious. (3) From the perspective of each member of the supply chain, the profit change of the manufacturer is more sensitive to the change of order quantity compared with the cost coefficient of carbon emission reduction. When the cost of carbon emission reduction technology is too high, manufacturers may not have much incentive to carry out technological research and development and innovation, resulting in failure to achieve system optimization. (4) This study designed a revenue-cost-sharing contract coordination mechanism; that is, the retailer will provide part of the revenue to the manufacturer, and the manufacturer will provide recovery compensation to the recycler.