Abstract: Fully homomorphic encryption has important application in cloud computing. However, the existing fully homomorphic encryption schemes share a common flaw that they all use public keys of large scales. And this flaw may cause inefficiency of these schemes in the key and identity management. To solve this problem, a certificateless fully homomorphic encryption scheme is presented based on Learning With Errors (LWE) problem. The scheme builds the connection between the users identity and its public key with the trapdoor one-way function with preimage sampling so that the certificates are no longer necessary. The private keys are chosen by the users without key escrow. In the random oracle model, the security of the scheme strictly reduces to hardness of decisional LWE problem.