Data owners' outsourced data on cloud data storage servers by the deduplication technique can reduce not only their own storage cost but also cloud's. This paradigm also introduces new security issues such as the potential threat of data lost or corrupted. Data integrity verification is utilized to safeguard these data integrity. However, the cloud deduplication storage only focuses on file/chunk level to store one copy of the same data hosted by different data owners, and is not concerned with the same part of different data, e.g., a series of version files. We propose an integrity verification algorithm of different version files. The algorithm establishes the generic storage model of different version control methods to improve the universality of data verification. Then, the methods of verification tags and proofs generating are improved based on the index pointers corresponding to the storage relationship in the version groups and chained keys. Finally, the random diffusion extraction based on the random data sampling in the version group is proposed to improve the verification efficiency. The results of theoretical and experimental analysis indicate that the algorithm can achieve fast and large-scale verification for different version data.