The large scale of construction in mega projects leads to significant environmental and socioeconomic impacts; thus, the projects should also exhibit greater social responsibility. Adopting green supply chain management in the construction process is an important way to realize the goal of sustainable development of mega projects. Because the green supply chain behavior during construction is mainly demonstrated by contractors, it is especially important to study the evolutionary trend of their behavior. Thus, to explore the cooperative relationship among contractors, this paper considers a lengthy construction period, multi-agent participation dynamics, and opportunistic behavior-all are key features of mega projects-and establishes an evolutionary game model. Specifically, a replicator dynamic equation is used to describe the long-term effects of the contractor's decisions. Equilibrium determinants are then analyzed and simulated. The results show that the initial probabilities of the two types of contractors (main contractor and subcontractor) demonstrating opportunistic behaviors have a significant effect on the direction of evolution of the mega project. The main contractor, who dominates the subsidy allocation by the government and project owner, should pay attention to maintaining a balance in the income distribution between him or her and the subcontractor. Additionally, there is an optimal distribution coefficient for the subsidy that minimizes the overall probability of opportunistic behavior. This paper provides a point of reference for the decisions of the main contractor and the subcontractor in the green supply chain of mega projects.