In recent years, with the country’s vigorous promotion of green buildings and the increasingly complex and large-scale engineering projects, the design-construction consortium model can better meet the needs of the organization and implementation of large-scale green projects and become a realistic choice for enterprises in project implementation. Therefore, the formation of a good and stable cooperative relationship between consortium members is increasingly important in improving project revenue and quality. The issue of maintaining the stability of consortium relationships is an urgent problem to be solved at this stage. As such, a three-party evolutionary game model, based on evolutionary game theory, comprising the developer unit, design unit, and construction unit, is constructed here. Then, strategies for ensuring evolutionary stability under different design modalities are discussed. Finally, the influence of relevant parameters under changing design conditions on the stability of the design and construction consortium of green building projects is analyzed through numerical simulation. The research results show the following: (1) If the additional revenue distribution coefficient within the consortium members is closer to 0.5, the influence on the stability of the design and construction consortium will be smaller; in contrast, if the influence on the design and construction consortium is increased, the cooperative relationship within the consortium will be more unstable. (2) The presence of additional revenue can increase the stability of the design and construction consortium. An increase in the additional revenue will inhibit the instability of the consortium on the one hand and strengthen the stability of the consortium on the other but will also lead to the occurrence of opportunistic behavior. (3) The construction unit’s payment of a subsidy to the cooperative members can help promote the stability of the design and construction consortium to a certain extent and can also weaken the effects of other factors on the stability of the consortium, but there is a threshold value for the amount of said subsidy. (4) On the one hand, the cooperation members actively cooperate with each other to maximize the cooperation benefits of the design and construction consortium, while on the other hand, the construction unit actively promotes the implementation of the green building project, strictly monitors the implementation of the green design and green construction approach by the design and construction units in the early and implementation stages of the project, prevents the design changes caused by the final product failing to meet the green building standard, and actively solves design change problems in a manner that benefits the sustainable development of the green building, so that the cooperative relationship among the members of the consortium can develop steadily, which is beneficial to the green and ecological development of architectural design and construction.