This paper invested a two-echelon construction supply chain that consists of a general contractor and a subcontractor. This paper constructs the centralized model and the decentralized models, respectively, and studies the emission reduction and revenue distribution strategies of construction supply chain considering fairness concern and cap-and-trade. Numerical analysis is carried out to analyze the influence of cap-and-trade and fairness concern on the optimal decision and the maximum profit of construction supply chain. This paper shows that, under cap-and-trade policy, the centralized model has the best emission reduction effect and the highest supply chain profit without fairness concern, while the general contractor’s Stackelberg model has the best emission reduction effect and the highest supply chain profit with fairness concern. In the two scenarios, the Vertical Nash model is the most unfavorable to emission reduction, and it will also seriously damage the interests of enterprises. In practice, supply chain should choose the general contractor’s Stackelberg model and avoid the Vertical Nash model. Because fairness concern of the subcontractor will damage the supply chain profits and emission reduction performance, the general contractor shall try to select the subcontractor with lower fairness concern to avoid the loss of profit. Besides, enterprises should actively take measures to reduce fairness concern, such as enterprises signing the contract price confidentiality clause, which aims to reduce fairness concern of the subcontractor. The results of this paper can not only enrich the research content of construction supply chain management, but also provide references for the government to formulate emission reduction policies.