With the continuous progress of China's economy and society， green development has become a national strategy， and carbon emission reduction is an important measure. The government can promote the investment of enterprises' emission reduction technology and increase social welfare through moderate low-carbon subsidies to enterprises. The introduction of block-chain technology into the low-carbon supply chain can improve the coordination degree of low-carbon decision-making among the main bodies of the supply chain and promote the emission reduction of enterprises. Therefore， it is of great significance to study the government subsidy strategy of low-carbon supply chain based on block-chain technology. In this paper， a two-level low-carbon supply chain composed of a manufacturer and a retailer is taken as the research object， and the government subsidy strategy of the low-carbon supply chain is taken as the research topic. The government invests in the construction of the application platform of block-chain technology， and the supply chain enterprises pay to use the block-chain technology. Under this background， considering consumers' low-carbon preference and green trust， this paper set up before and after the application block chain technology under R&D investment subsidy policy or output subsidy policy of these four situations of three stages Stackelberg game models， in which the government takes the lead and manufacturers and retailers follow and the government to the social welfare maximization as the goal， manufacturers and retailers in order to maximize their own interests as the goal， through comparing the four kinds of situations of the optimal rate of social welfare， carbon reduction and low carbon product production， discusses the government low carbon subsidies strategy of optimal problem. And the validity of the results is verified through the analysis of examples. The results show that when the product of consumers' low-carbon preference coefficient and green trust coefficient is greater than a certain fixed value， the government can obtain higher social welfare through output subsidies， and promote enterprises to reduce emissions more effectively. Governments have been able to boost demand for low-carbon products through output subsidies. When the cost coefficient of emission reduction approaches infinity， the demand for low-carbon products when the government implements output subsidies is 4 times that when the government implements R&D investment subsidies. When the single-cycle cost sharing of block-chain platform and the unit cost of enterprises' application of block-chain technology are less than a certain threshold， the government's construction of block-chain platform can obtain higher social welfare， promote enterprises' emission reduction and improve consumers' demand for low-carbon products. Therefore， the government should increase investment in science and technology， and to make efforts to reduce the block chain platform construction cost and prolong the cycle of block chain platform， for low carbon green products to create a fair， just and open market environment， and control technology of enterprise application block chain unit cost within a reasonable range， encourage enterprises to actively application block chain technology， in order to obtain higher social welfare.
