Focused on the flaw of large-scale public keys which is shared by the existing fully homomorphic encryption schemes, the idea of certificateless public-key encryption was introduced into the design of fully homomorphic encryption schemes, and an certificateless fully homomorphic encryption scheme was proposed. The overall efficiency of the cryptosystem would be improved since the public keys of the scheme no longer need identity authentication. The full-rank differencing matrix was used to embed the identities into the scheme, and the random oracles were no longer needed in the security proof because of the absence of hash function. The partial private keys were abstracted by a pair of dual normal distribution sampling functions, and were transformed to the private keys by the instance of learning with errors problem. The scheme employed double encryption to deprive the servers of the capability of decryption and thus avoided key escrow. The security of the scheme reduces to the hardness of learning with errors problem.