Most existing attribute-based keyword search schemes only support monotonic access structure and lack efficient verification for search results. Aiming at these problems， a ciphertext keyword search attribute-based encryption scheme with verifiable search and non-monotonic access structure was proposed. Firstly， the polynomials were constructed by the attribute values， and the fine-grained ciphertext search permission setting was accomplished by divisibility property of the polynomials. Then， both keyword search and outsourced decryption were performed by the cloud servicer without revealing any private information. Finally， the search result verification was realized by utilizing the proposed commitment scheme. The proposed scheme supports multiple functions such as non-monotonic access structure， fine-grained search， data sharing， outsourced decryption， and verifiable search. Under the augmented Multi-Sequence of Exponents Decisional Diffie-Hellman （aMSE-DDH） assumption， it can be proved that this scheme has selective indistinguishability security under chosen ciphertext attacks and under chosen keyword attacks， respectively， in the random oracle model. Experimental results show that the terminal decryption time of the proposed scheme is not related to the attribute number， and is about 12.9 ms.