Blockchain-enabled cold-chain logistics system (BCCLS) has well solved the centralized problem in traditional systems. However, along with that different logistics entities establish their own distributed blockchain ledger, which brings new “data island” and privacy leakage problems for BCCLS. In this paper, a transaction ring signing model with a multi-chain fusion mechanism has been introduced first which helps to achieve secure cross-chain data sharing. Meanwhile, a ring signature (RS) scheme is proposed with lattice assumption, which can protect the user privacy and cross-chain transactions. The lattice hard problem improves the anti-quantum security of the transaction ring signing model. Then, the security proof has been executed with random oracle model, and the results show that this RS scheme can get anonymity under full key exposure and unforgeability under insider attack. The efficiency comparison and performance evaluation show the efficiency and practical of the proposed multi-chain fusion model and RS scheme.