Public key encryption with keyword search (PEKS) technology achieves accurate ciphertext retrieval while protecting data privacy. However, curious or malicious semi-trusted cloud servers can cause privacy breaches, which bring a trusted problem of ciphertext management and searching. To address this problem, we present trusted certificateless authentication public-key encryption with keyword search scheme in cloud storage(TCA-PEKS), which ensuring trusted retrieval, simultaneously resolve the problems of key escrow and certificate management that exists in PEKS. In the scheme, the security of ciphertext storage and verification is strengthened based on blockchain non-tampering feature, which can assist users to verify the correctness of the file. Especially, we construct an open and transparent smart contract to limit the malicious behavior of cloud servers, in which the user’s complete private key splits the secret value and the partial private key, further guarantees the correctness of the retrieval process. Finally, the scheme is proved to satisfy ciphertext and trapdoor indistinguishability under the random oracle model, and the performance evaluation results show that the scheme is highly efficient.