With the rapid development of cloud computing, cloud storage is widely used. In the cloud environment, users’ virtual machine system mirrors and data are stored in the cloud server. The escape of virtual machines and Trojan virus attacks make it challenging to ensure the integrity of virtual machine systems. Trusted computing is expensive to randomly verify data integrity and does not adapt to dynamic data changes. Provable data integrity is a potential solution to this problem. Merkle Hash Tree (MHT) model is widely adopted in provable data integrity. Although MHT requires only a small amount of evidence for verification, the verifier’s number of hash calculations and the server’s efficiency of evidence query are not optimal. Moreover, the verification frequency of each piece of data is not considered by MHT. Properly handling these factors can improve the actual verification performance. In this paper, a lightweight and efficient data integrity verification approach called HB+-MHT is proposed for the tenant virtual machine (TVM) in cloud computing. In HB+-MHT, the Huffman hash tree scheme is used for small file verification to ensure that the hot file has a shorter path, which reduces the required amount of evidence for verification. Meanwhile, the B+ hash tree scheme is used for big files verification, which can effectively reduce evidence query time and hash calculation times. The experimental results show that the scheme proposed in this paper can perform data integrity verification well, with reduced computing and storage overhead.