Under the context of low-carbon, upstream manufacturers and downstream retailers work together to improve the low-carbon reputation. Considering low-carbon and recycling subsidies, differential game models are constructed under decentralized and centralized cases by taking the level of low-carbon reputation as a state variable. Through comparison analysis, a profit-expense sharing contract is designed to improve the efficiency of the supply chain. The result shows that, 1) In each case, the level of low-carbon reputation increases with time and gradually reaches a stable state. 2) Dual subsidy policies not only encourage the manufacturer's low-carbon behaviors, but also contribute to the low-carbon reputation and member's profit. However, the retailer's low carbon publicity level will not be affected. 3) The decentralized case leads to the loss of supply chain efficiency, and keeping the manufacturer's profit-sharing ratio lower than the cost-sharing ratio can improve low-carbon reputation after coordination. In addition, the manufacturer sharing more low-carbon publicity costs can improve the profits of supply chain members when meeting conditions.