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To improve the security of the data on cloud storage, numbers of data integrity auditing schemes have been proposed in the past several years. However, there only a few schemes considered the security challenge that the user's key is exposed unknowingly which is very likely to happen in real-life. To cope with the problem, we propose a public data integrity auditing scheme for cloud storage with efficient key updating. In our scheme, the user's key is updated periodically to resist the risk of key exposure. Meanwhile, the authentication tags of blocks are updated simultaneously with the key updating so as to guarantee the data integrity can be verified normally. The algorithm of key updating in our scheme is very efficient which only needs a hash operation while previous schemes need two or three exponentiation operations. Moreover, the workload of tag updating is undertaken by cloud servers with a re-tag-key which reduces the burden of users and improves the efficiency of the scheme. The communication cost of the scheme is also reduced greatly, for instance, the information size in ‘re-key’step is decreased from two group members to one. Furthermore, we give the formal security model of our scheme and prove the security under the CDH assumption. The experimental results show that our proposal is efficient and feasible.