To address the problem of multi-cycle carbon emission reduction in the supply chain under double carbon goals, a multi-cycle supply chain model consisting of a single manufacturer and a single retailer was proposed to study the coordination and optimization between the carbon emission reduction level and retail pricing in each cycle. Firstly, a single-cycle Stackelberg game model was established and a dynamic planning model was constructed based on the game model for coordinated decision-making in multi-cycle supply chains. Secondly, the Stackelberg game was used to solve the retail and wholesale prices of products in each cycle. After that, the optimal level of carbon emission reduction for each cycle was solved by dynamic programming and the maximum profit of manufacturers and retailers in multiple cycles was derived. The influence of factors such as carbon emission reduction cost coefficient and low carbon preference degree on carbon emission reduction, pricing decisions, and profit of manufacturers and retailers was obtained by example analysis. The results show that the carbon emission reduction of manufacturers in each cycle is positively correlated with the number of cycles remaining and the degree of low carbon preference and is negatively correlated with the emission reduction cost coefficient; the wholesale price and retail price in each cycle have a negative relationship with the low carbon preference degree of consumers and the emission reduction cost coefficient; the wholesale and retail prices of each cycle gradually increase as the cycle goes on.