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The smart grid is considered to be the next-generation electric power network. In a smart grid, there are massive data to be processed, so cloud computing is introduced into it to form a cloud-based smart grid data management system. However, with data no longer being stored locally, how to ensure the integrity of data stored in the cloud in the smart grid has become an urgent problem awaiting solution. Provable data possession has been proposed to solve this problem. With the development of quantum computer technology, quantum attacks-resistant cryptographic schemes are gradually entering people’s horizons. Lattice cryptography can resist quantum attacks. In this article, a lattice-based provable data possession scheme is proposed for cloud-based smart grid data management systems. The scheme is proved unforgeable under the small integer solution hard assumption in the standard model. Compared with other two efficient lattice-based provable data possession schemes in the standard model, our scheme also shows efficiency.