Key exchange protocol allows two or more users to compute share session key via exchange information in the open communication channel, and uses the session key to finish cryptography tasks, such as secure communication and authentication. Recently, it becomes a hotspot research question that how to design authenticated key exchange protocol with lattice-based one-way function. Several lattice-based two-party authenticated key exchange protocols have been proposed. However, how to extend them to the identity-based cryptography background still remains open question. In this paper, an identity-based authenticated key exchange protocol from the learning with errors (LWE) problem over cyclotomic ring is proposed. The protocol generates master key by ring LWE (RLWE) sample algorithm, and further extracts the users’ secret key, and computes key materials which derive the share session key via exchanging Diffie-Hellman ephemeral key. The protocol introduces error item, uses encoding bases of ideal lattice as the tool for analyzing error tolerance, and makes reasonable suggests for parameters setting. The protocol achieves provable AKE secure and PKG forward secure in the ID-BJM model. Furthermore, the session key is also secure even if both long private keys are leaked or both ephemeral private key are leaked or A’s ephemeral key and B’s long private key are leaked.