As medical data become increasingly important in healthcare, it is crucial to have proper access control mechanisms, ensuring that sensitive data are only accessible to authorized users while maintaining privacy and security. Ciphertext-Policy Attribute-Based Encryption (CP-ABE) is an attractive access control solution that can offer effective, fine-grained and secure medical data sharing, but it has two major drawbacks: Firstly, decryption is computationally expensive for resource-limited data users, especially when the access policy has many attributes, limiting its use in large-scale data-sharing scenarios. Secondly, existing schemes are based on data users’ attributes, which can potentially reveal sensitive information about the users, especially in healthcare data sharing, where strong privacy and security are essential. To address these issues, we designed an improved CP-ABE scheme that provides efficient and verifiable outsourced access control with fully hidden policy named EVOAC-HP. In this paper, we utilize the attribute bloom filter to achieve policy hiding without revealing user privacy. For the purpose of alleviating the decryption burden for data users, we also adopt the technique of outsourced decryption to outsource the heavy computation overhead to the cloud service provider (CSP) with strong computing and storage capabilities, while the transformed ciphertext results can be verified by the data user. Finally, with rigorous security and reliable performance analysis, we demonstrate that EVOAC-HP is both practical and effective with robust privacy protection.