The continuous increase in the number of transactions is exerting significant pressure on the storage capacity of blockchains. By storing data on multiple blockchains and interacting with each other with cross-chain technology, the storage pressure can be relieved to a large degree. Nevertheless, the feature of immutability may impede the further development of blockchains, e.g., some expired identity information cannot be updated due to immutability. The decentralized chameleon hash function can resolve the issue while ensuring the feature of decentralization. Unfortunately, how to ensure the consistency of dynamic data updating in cross-chain interaction is still a question worth considering. In this paper, we propose a dynamic cross-chain decentralized data consistency verification (DCCV) model, in which we adopt an audit chain and design a dynamic Merkle hash tree to guarantee the consistency of dynamic data updating between the source chain and the target chain. In addition, in order to enhance the relevance of calculations across different smart contracts and improve audit efficiency, we propose a way to develop cross-chain smart contracts collaboratively. Moreover, Cosi protocol and multi-signcryption are utilized to ensure the security and privacy of cross-chain data transmission. Finally, theoretical and experimental analysis demonstrates that DCCV can achieve dynamic data consistency verification in the process of cross-chain interaction