Abstract Our paper constructs a low‐carbon supply chain (LSC) with a single manufacturer producing low‐carbon products and a single retailer. Assume that the retailer possesses private demand information and consider two cases: The manufacturer or the retailer determines the low‐carbon product's retail price. By constructing principal‐agent models, we obtain the optimal menu of contracts in each case. The impacts of the carbon tax rate and information asymmetry on LSC members' equilibrium solutions and expected profits are discussed. The results show that, given certain conditions, both the LSC members may obtain more expected profits under information asymmetry by introducing appropriate contracts.