Periodic audit of data stored on cloud servers is a core strategy to ensure the security and integrity of cloud-stored data. It can identify and address the risks of data tampering or loss effectively. However， traditional public audit schemes suffer from issues such as certificate management or key escrow， leading to privacy leak problem during data querying and dynamic modification. Furthermore， with the continuous development of quantum computing technology， public audit schemes based on traditional public key systems face serious threats of being cracked by quantum computers. To address the above issues， a post-quantum certificateless public audit scheme based on lattice was proposed. Firstly， a certificateless public key cryptosystem was used to solve the certificate management and key escrow problems in traditional public audit schemes. Secondly， during data querying and dynamic modification processes， Data Owners （DO） were not required to provide specific data block information， thereby ensuring the privacy of the DO. Finally， lattice cryptography technology was employed to resist attacks from quantum computers. Theoretical analysis and experimental comparison results demonstrate that the proposed scheme can resist malicious attacks while ensuring the privacy of DO operations， and it achieves higher efficiency in label generation.