The complex and changeable external pressures such as government regulations and consumer demand bring challenges to emissions abatement in supply chain. For the asymmetric information between manufacturer and consumer caused by the hidden low-carbon preference and the various carbon policies, this research, based on principal-agent model, constructs three models including the benchmark model without carbon policy, the abatement contract models with single abatement mechanism and multiple abatement mechanism, designs the abatement contract and the single and multiple abatement mechanisms, aiming to improve abatement efficiency and realize low emissions of supply chain. We find that information rent caused by asymmetric information between manufacturer and consumer is the main impact factor of reducing abatement efficiency of supply chain, and the purpose of the abatement contract is that there is not the motivation for consumer to falsely report preference information and accurate consumer demand is obtained by manufacturer. Additionally, although single abatement mechanism can promote manufacturer to reduce emissions, the extra cost caused by carbon tax leads to negative utility to manufacturer. Multiple abatement mechanism can reduce the negative effect of single abatement mechanism on manufacturer and make it obtain more revenue. The research provides a reference for manufacturer in supply chain how to cooperate with government and consumer who possess private information.