This paper takes the secondary low-carbon supply chain composed of a manufacturer and a retailer as the research object and takes the government subsidy strategy of low-carbon supply chain as the research theme, the government invests in the construction of blockchain technology application platform, and supply chain enterprises use blockchain technology for compensation. Under this background, considering consumers’ low-carbon preference and green trust, a three-stage game model dominated by the government and followed by manufacturers and retailers under the four scenarios of emission reduction technology input subsidy and low-carbon product output subsidy before and after the application of blockchain technology is established. By comparing the optimal social welfare, carbon emission reduction rate, and low-carbon product output under the four scenarios, the optimal problem of government low-carbon subsidy strategy is discussed. It is found 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 and promote enterprises’ emission reduction through output subsidies. The government can always promote the demand for low-carbon products through output subsidies. When the emission reduction cost coefficient approaches infinity, the demand for low-carbon products when the government implements output subsidies are four times that when the government implements technology subsidies. When the single cycle shared cost of the blockchain platform and the unit cost of enterprise application of blockchain technology are less than a certain threshold, the government’s construction of the blockchain platform can obtain higher social welfare, promote enterprise emission reduction, and improve consumers’ demand for low-carbon products.