Benefited from cloud storage services, users can save their cost of buying expensive storage servers. Meanwhile they lost the physical control of their data. So effective methods are needed to verify the correctness of the data stored in cloud servers, which are the research issues the provable data possession (PDP) faces. This paper analyzes the existing PDP algorithms, finds some defects of these algorithms, such as highly computing cost, a limited number of challenge. Then proposes code-based provable data possession scheme for integrity verification based on homomorphic code-based hash function, the advantage of homomorphic hash function is providing provable data possession and data integrity protection. The scheme is a good way to ensure the integrity of remote data and to reduce redundant storage space and bandwidth consumption. The major cost of the scheme is in the server side, it is suitable for mobile devices under cloud storage environments. We prove that the scheme is feasible by analyzing the security and performance of the scheme, most of all, the scheme can resist the attack of post-quantum computers.