Due to its decentralized, tamper-proof, and trust-free characteristics, blockchain is used in the Internet of Things (IoT) to guarantee the reliability of data. However, some technical flaws in blockchain itself prevent the development of these applications, such as the issue with linearly growing storage capacity of blockchain systems. On the other hand, there is a lack of storage resources for sensor devices in IoT, and numerous sensor devices will generate massive data at ultra-high speed, which makes the storage problem of the IoT enabled by blockchain more prominent. There are various solutions to reduce the storage burden by modifying the blockchain's storage policy, but most of them do not consider the willingness of peers. In attempt to make the blockchain more compatible with the IoT, this paper proposes a storage optimization scheme that revisits the system data storage problem from a more practically oriented standpoint. Peers will only store transactional data that they are directly involved in. In addition, a transaction verification model is developed to enable peers to undertake transaction verification with the aid of cloud computing, and an incentive mechanism is premised on the storage optimization scheme to assure data integrity. The results of the simulation experiments demonstrate the proposed scheme's advantage in terms of storage and throughput.