Many sophisticated cloud platforms are available to provide services such as storage and computation for Internet of Things (IoT) applications. However, with the concerns about the semi-trusted nature of cloud platforms, data security and privacy have been gaining broad attention. In this paper, we propose a blockchain-assisted verifiable data sharing scheme (BAV-DSS) for IoT. The BAV-DSS features fine-grained access control, fast encryption, and outsourced decryption with verifiability. Specifically, with the application of ciphertext-policy attribute-based encryption (CP-ABE), flexible access control is enabled. Blockchain is employed to store public keys, generate account addresses, and perform data verification. Furthermore, the selective replayable chosen ciphertext attacks (sRCCA) security of BAV-DSS is proved, and the simulation results indicate that BAV-DSS obtains high efficiency and practicality compared to other schemes.