In this paper, we first present a concrete formal protocol design approach, which is based on authentication tests, to create an Efficient and Secure Internet Key Exchange (ESIKE) protocol. Then we formally prove the secure properties of ESIKE with strand space model and authentication tests. The ESIKE protocol overcomes the security shortages of the Internet Key Exchange (IKE), and can provide secure negotiation of session key and Security Association (SA), protection of endpoints' identities, and mutual authentication between the initiator and the responder. It needs only three messages and less computational load, so it is simple and efficient.