In this paper, we study the supply chain coordination problem between a manufacturer and a retailer regarding consumers' low-carbon preferences. The retailer considers the market demand to determine the order quantity; the manufacturer chooses how to reduce emissions according to the retailer's order quantity. We consider four cases, including the non-emission abatement, the emission abatement of decentralized decision-making, the centralized decision-making and the retailer providing a cost-sharing contract. By comparing the four cases, we find that the case of a retailer providing a cost-sharing contract can coordinate the supply chain, achieving a Pareto improvement for the manufacturer and retailer. In addition, we use the Rubinstein bargaining model to determine the cost-sharing ratio. Finally, numerical simulations are given to analyze the impact of the cost-sharing ratio on the equilibrium results, including the profit and the emission abatement level. Furthermore, we investigate the impact of the cost-sharing ratio and consumers' low-carbon awareness on the profits of the members in the supply chain. We find that the equilibrium results, including the order quantity, the emission abatement level and the profits of the members in the supply chain under contract, are higher than the ones under centralized decision-making. The results show that in the higher low-carbon awareness market, retailers should formulate a reasonable cost-sharing ratio to achieve emission reduction coordination.