Abstract This study considers a low‐carbon supply chain (LSC) comprising one supplier and one manufacturer with yield uncertainty under the carbon‐trading policy, where the manufacturer holds private carbon emission reduction cost coefficient information. Two trade schemes are examined under information asymmetry, namely, the contract menu for information screening and the wholesale price contract. A further scenario is analyzed in which blockchain is adopted to eliminate information asymmetry and enhance the consumers purchasing willingness. The results indicate that the thresholds for LSC members to prefer blockchain adoption vary across different trade schemes. Even so, blockchain adoption can achieve Pareto improvements for the LSC members’ ex ante profits within certain ranges, regardless of the trade scheme. Notably, a conclusion highlights that there exist ranges in which the LSC members may not prefer blockchain adoption, although the unit blockchain adoption cost equals zero.