As a major energy consumption sector in China, the construction industry has been a hot spot of concern regarding carbon reduction. The local governments have launched various policies to promote low-carbon production. However, the response of different parties is still confusing. Thus, based on prospect theory, this paper investigated the relationship among government policy intervention, enterprises’ production strategies and consumers’ purchasing behavior. Then, a tripartite evolutionary game model was established and a case study was applied to simulate the model. The results show that: 1) government subsidies and penalties can directly influence the strategy of each party, but excessive supervision costs can also be counterproductive to policy intervention; 2) corporate revenue and technical costs are also the main drivers affecting the low-carbon strategies of construction enterprises; 3) enhancing consumers’ environmental preference or awareness is also an effective way to promote low-carbon production. The findings are valuable for governments to further realize related parties’ responses to different policies and make appropriate development for low-carbon construction.