A key exchange (or agreement) protocol is designed to allow two entities establishing a session key to encrypt the communication data over an open network. In 1990, Gunther proposed an identity-based key exchange protocol based on the difficulty of computing a discrete logarithm problem. Afterwards, several improved protocols were proposed to reduce the number of communication steps and the communicational cost required by Gunther's protocol. This paper presents an efficient identity-based key exchange protocol based on the difficulty of computing a discrete logarithm problem. As compared with the previously proposed protocols, it has better performance in terms of the computational cost and the communication steps. The proposed key exchange protocol provides implicit key authentication as well as the desired security attributes of an authenticated key exchange protocol.