Attribute-based encryption (ABE) has been widely applied in cloud services for access control. However, a large number of pairing operations required for decryption affect the wide use of ABE on lightweight devices. A general solution is to outsource the heavy computation to the cloud service provider (CSP), leaving the lighter computation to the data user. Nevertheless, it is impractical to assume that the CSP will provide free services. A recent ABE scheme with payable outsourced decryption ABEPOD (TIFS’20) provides a solution for the above payment issue. The CSP is generally untrusted, however, ABEPOD does not offer a verification mechanism for the data user to verify the correctness of the message. Moreover, the use of dual key pairs in ABEPOD incurs a significant computational overhead for data users during the key generation phase. We address the above issues by presenting a new blockchain-based verifiable outsourced attribute-based encryption system that enables data users to verify the correctness of plaintexts. We implement batch verification using homomorphic technical to optimize the verification process. We use the technique of dichotomous search to accurately locate problematic plaintexts. Additionally, we optimize three key-generation algorithms to transfer the computational cost from the data user to the key generation center. We offer the formal security models and the instantiation system with security analysis. As compared to ABEPOD, we further optimize the key-generation algorithms such that the computational overhead of transformation-key and verification-key generation for data users is reduced from O(Ω) to O(1) and reduced by half respectively, where Ω is the number of attributes.