With the growing low-carbon economy and people's preference for low-carbon products, building carbon emission reduction(CER) has also been highly concerned by the government. With the government as the main body, we use differential game to analyze the impact of carbon tax and cost subsidy policy on building's CER. We get: compared with carbon tax policy, carbon tax and cost subsidy policy are more conducive to reduce carbon emission; When the cost subsidy rate is less than a fixed value, the cost subsidy and carbon tax policy is the optimal strategy for building's CER. When the cost subsidy rate is greater than a fixed value, the cost subsidy policy is the optimal strategy for building's CER.