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In order to study how to promote the collaborative innovation of green building projects of construction enterprises, this paper establishes an evolutionary game model of suppliers’ participation in collaborative innovation of green building projects of construction enterprises under government governance. Through a numerical simulation, our research analyzes the influence of government tax preference, government infrastructure construction, and environmental pollution punishment on the behavior of the government, suppliers, and construction enterprises. The empirical research shows that the government’s tax incentives will continue to encourage suppliers to choose collaborative innovation. If the government’s short-term tax incentives are small, construction enterprises will evolve in the direction of midway betrayal. When the government’s long-term tax incentives are large, construction enterprises will evolve in the direction of the collaborative innovation of green building projects. Furthermore, the government’s infrastructure support for suppliers to participate in collaborative innovation of green building projects of construction enterprises will encourage suppliers and construction enterprises to choose green building projects for collaborative innovation. With the continuous maturity of green building projects in the construction market, the government has evolved from positive governance to negative governance. The government will take the opportunity to give up infrastructure construction and turn to other supporting policies. Lastly, a low intensity of environmental pollution punishment makes it difficult to promote the construction enterprises to evolve in the direction of collaborative innovation. A moderate intensity of environmental pollution punishment can encourage construction enterprises to evolve in the direction of collaborative innovation, while high-intensity environmental pollution punishment can encourage construction enterprises to choose the direction of midway betrayal. Environmental pollution punishment has no significant impact on suppliers’ selection of collaborative innovation of green building projects in the short term.