We propose an access control encryption (ACE) scheme which supports the fully homomorphic operations on the ciphertext,and give a concrete construction from Learning with Error (LWE).Firstly,we show the definition and security model of ACE supporting the fully homomorphic operations under the ciphertext according to the concept of the fully homomorphic encryption (FHE) and ACE.Secondly,we make a black-box construction based on the fully homomorphic encryption which satisfies the certain conditions.Finally,we show a concrete construction based on LWE.