The Internet of Things (IoT) is one important digital revolution in both the academic world and commerce. It brings convenience to people`s daily lives; but, the challenges of security and privacy have become a very big task in IoT. Attaining safety and data integrity verification of information in IoT networks is one of the hot topics for future IoT applications. The provision of security to any information in an IoT network is a big challenge, which must be given the top priority for many current and future applications of IoT. Traditional data integrity verification approaches only use encryption algorithms to secure information, depending on Third-Party Auditors (TPAs). The blockchain's basic principle is that information produced by users or nodes is tested for accuracy and cannot be altered once it is updated on the blockchain. Blockchain based data integrity schemes can effectively overcome TPA's issues. In this paper, we propose a blockchain based data integrity technique with a bilinear design for IoT information. We achieve data integrity according to the characteristics of bilinear design in the form of blockchain communications. The proposed blockchain based framework for data integrity verification consists of different entities such as client, Key Generation Centre (KGC), cloud storage server, and blockchain. Proposed data integrity verification operates in three stages: Setup stage, Processing stage and Verification stage. Simulation results show that the performance of the proposed blockchain approach for data integrity in IoT is better as compared with the blockchain based cloud data integrity verification scheme with high efficiency (DICF). The results demonstrate that our scheme is better interms of signature generation time, end to end delay, memory utilization as compared to DICF.