Whether in the case of information symmetry or information asymmetry, cost sharing is a way to promote enterprises of the low-carbon supply chain to actively cooperate and coordinate, and the behavior preference of decision-makers will affect the process. On the basis of consumers' low-carbon preference, this paper discusses cooperation strategies of the supply chain led by retailers after low-carbon investment. We show how different cost sharing contracts influence wholesale price, retail price, the optimal profit and the sharing proportion of low-carbon costs based on the different information sharing models. The results show that low-carbon investment can promote an increase in all enterprises' profits in the supply chain, but the results under the decentralized decision are not better than those under the centralized decision. Therefore, this study designs low-carbon costs sharing contracts to coordinate decisions. When the cost sharing proportion is within a reasonable range, the single-cost sharing contract can improve the profit of the supply chain. However, the profit of the entire supply chain is still lower than that under the centralized decision, which fails to achieve the perfect coordination of the low-carbon supply chain. When retailers misstate low-carbon costs and dominate the supply chain, they will prefer to understate the low-carbon promotion cost to maximize their profits. Through further calculation, when enterprises use innovation-promotion costs sharing contracts, we can find that the results under the centralized decision are equal to those under the decentralized decision. Therefore, the innovation-promotion costs sharing contract can realize the perfect coordination of the low-carbon supply chain and promote the cooperative decision-making of upstream and downstream enterprises.