Logistics supply chain (LSC), a chain structure that integrates and coordinates all logistics transactions, has become an essential component of the modern logistics industry. By using blockchain, trusted logistics services enable participants to effectively record and track transactions during the logistics process. Current blockchain‐based LSC features distributed structure and data privacy requirements, hindering the supervision of logistics transactions. Leveraging emerging dual‐blockchain architecture to separate logistics transactions from supervision is a promising direction. However, the dual‐blockchain collaboration restricts supervision due to its cross‐chain privacy and efficiency. To address these issues, a logistics supply chain supervision scheme based on dual‐blockchain collaboration (DBC) is proposed. First, an independent supervision blockchain is constructed to balance the contradiction between distributed structure and supervision requirements. Second, two mechanisms are designed to enhance the privacy and performance of collaborative supervision. The hybrid access control mechanism enables fine‐grained supervision for different participants, and the aggregated transaction verification method supports efficient collaboration for logistics transactions. Security analysis and performance evaluation demonstrate the feasibility of DBC in enhancing the security and supervision of logistics data on the dual‐blockchain architecture. Experimental results show that the cross‐chain supervision overhead of DBC is reduced to of the baseline schemes.