Climate change has become a pressing concern in recent decades, and the reduction of greenhouse gas emissions is now recognised as an important strategy for redressing that concern. The carbon trading system and the provision of low-carbon cost subsidies are essential measures for reducing emissions in various countries and regions. In this context, we study the investment decision of emission reduction technology in a supply chain composed of a leading manufacturer and a following retailer under the cost subsidy policy of carbon emission reduction. We consider consumers’ low-carbon preferences and utilise differential game theory and dynamic optimisation technology to construct the investment game model under a cost subsidy policy affecting manufacturers and retailers. We then identify the equilibrium strategy and the evolution path of emission reduction, profit, and social welfare according to the interest’s composition and game relationship of each stakeholder. We also use numerical simulation method to analyse the evolution path of the system and the sensitivity of related parameters, so as to determine the influence of related parameters on the structure and path of the system. We conclude that under the current carbon trading system, the cost subsidy policy implemented by the government plays a positive role in promoting emission reduction investment and corporate profits of supply-chain-related enterprises.