Provable data possession (PDP) is an important integrity checking technique in cloud storage. By using PDP, the client moves its data to cloud server and checks the possession of the data with constant computation. However, the client sometimes is not available to check its data possession. For example, the client wants to check its data which are stored in cloud server when he is in prison or at sea. In those cases, a convenient way to delegate the power of checking data possession to a proxy is necessary. In order to solve this problem, we propose a new provable data possession based on partial delegation (PDPPD). The PDPPD system model and security model are based on bilinear pairing and partial delegation. And the major feature of the proposed scheme is following: the client can delegate verification power to the proxy by sharing the converted secret key with the proxy, and the client can revoke or delete the proxy in an easy way at any time. Through our security analysis, the proposed scheme is provably secure. Compared with existing PDP schemes, the proposed scheme has less computation and communication overhead with the same level of security and also has wider application scenarios.