This paper designs a security model of the public key authenticated searchable encryption scheme in efficiently authoried certificateless environments, and proposes a specific certificateless public key authenticated searchable encryption scheme with efficient authorization. In this scheme, the cloud server uses the signature of the data owner on the ciphertext keyword index to verify the data owner identity. Secondly, the data user authorizes the authorization server to verify the identity of the data user. If the data user is legal, the server help the data user to verify the validity of the ciphertext returned by the cloud server. At the same time, the data owner and the data user use the cloud server public key to generate the ciphertext keyword index and the trapdoor search credentials that satisfies  the transmission security on the public channel. Finally, the efficiency of the proposed scheme is verified by experimental simulation.