With the development of Internet of things (IoT), more and more intelligent terminal devices outsource data to cloud servers (CSs). However, the CS is not fully trusted, and the heterogeneity among different domains makes it difficult for third-party auditor (TPA) to conduct an efficient integrity auditing of outsourced data. Therefore, the cross-domain data cloud storage auditing scheme based on certificateless cryptography is proposed, which can effectively avoid the big burden of certificate management or key escrow problems in identity-based cryptography. At the same time, TPA can effectively audit the integrity of outsourced data in different domains. Formal security proof and analysis show that the cloud storage auditing scheme satisfies the security and privacy requirements. Performance analysis demonstrates that the efficiency is acceptable.