Ciphertext-policy attribute-based encryption (CP-ABE) can provide fine-grained access control while guaranteeing data privacy. Considering that the existing CP-ABE-based access control schemes can not effectively address critical data security in edge computing, this study proposes a blockchain-based lightweight access control scheme over ciphertext (BLAC) in edge computing. In BLAC, a lightweight CP-ABE algorithm based on elliptic curve cryptography is designed, and fast elliptic curve scalar multiplication is adopted to realize algorithm encryption and decryption. Additionally, most of the encryption and decryption operations are securely transferred to make user devices with limited computing power efficiently complete the fine-grained access control process of ciphertext data with the assistance of edge servers. Meanwhile, a distributed key management method based on blockchain is designed, which enables multiple edge servers to collaboratively distribute private keys for users by blockchain. Security analysis and performance evaluation show that BLAC can guarantee data confidentiality, resist conspiracy attacks, and support forward security. Additionally, it has high user-side computational efficiency and low server-side decryption overhead and storage overhead.