Green buildings are considered to be an effective way to save energy, reduce emissions, and protect the environment. As one of the main bodies of green building construction, the construction unit’s willingness to build seriously affects the promotion of green building. Therefore, based on the viewpoints of natural persons and bounded rationality, this study constructs an evolutionary game analysis model, analyzes the impact of local government subsidy policies on the application strategies of construction units, and analyzes the steady-state and selection strategies. The system dynamics model is established using a flow chart, and the simulation results show that, in the long run, increasing the government subsidy and inspection cost cannot improve the application probability of the construction unit. Furthermore, the inspection intensity of the government and the indirect income of the construction unit has a direct influence on the application probability of the construction unit. The results show that the government should adjust the amount of the subsidy reasonably, improve the penalty mechanism, reduce development costs, strengthen publicity, and encourage construction units to actively apply for green buildings, so as to realize the transformation and upgrade of China’s construction industry.