Public key encryption scheme with keyword search (PEKS) enables us to search the encrypted data in a cloud server with a keyword, and no one can obtain any infor-mation about the encrypted data without the trapdoor corresponding to the keyword. The PEKS is useful to keep the management of large data storages secure such as those in a cloud. In this paper, to protect against quantum computer attacks, we present a lattice-based identity-based encryption scheme with key-word search. We have proved that our scheme can achieve ciphertext indistinguishability in the random oracle model, and our scheme can also achieve trapdoor security. In particular, our scheme can designate a unique tester to test and ret the search results, therefore it does not need a secure channel. To the best of our knowledge, our scheme is the first iden-tity-based encryption scheme with keyword search from lattice assumption.