Under the carbon tax policy, the vehicle remanufacturing has become popular, which threatens the new vehicle market. Facing the complicated competitive environment, the automobile manufacturer always adjusts product modular design to deal with the challenges from the internal and external remanufacturing. Currently, considering the impacts of the complicated market competitions and product modular design on the enterprise's operation management, how the carbon tax policy affects the vehicle remanufacturing is still uncertain. Thus, we construct a duopoly remanufacturing competition model consisting of an automobile manufacturer and remanufacturer with the aim of maximizing profit and determine the optimal product modular design, production, and remanufacturing decisions as well as profits. Then, we explore the impacts of the carbon tax on the vehicle remanufacturing supply chain from the perspectives of the economic, environment, and consumer surplus. The results show that the carbon tax is always disadvantageous to automobile manufacturer's profit but may benefit the automobile remanufacturer's profit. Contrary to the intuition, improving the carbon tax is not always conducive to the environment and harmful to the consumer.