Machine‐to‐machine communications have been actively engaged in by the standardisation and industry areas, also defined as machine‐type communication (MTC) in the release 10 of the 3rd Generation Partnership Project. The scenarios of 3rd Generation Partnership Project have been regarded as the promising solution facilitating machine‐to‐machine communications, which is being standardised as an emphatic application to be supported by long‐term evolution advanced. In this paper, we propose a novel group access authentication and key agreement protocol for MTC devices, which effectively reduces authentication costs compared with conventional schemes. In our proposed protocol, the first MTC device accessing the network performs a full authentication and key agreement authentication procedure and obtains a group temporary key and group authentication information on behalf of other MTC devices in the same group; then, the remaining MTC devices perform a simplified authentication procedure locally. The key derivation and group member joining and leaving are also discussed. Finally, the security of the proposed protocol is verified by using the AVISPA toolkit, and extensive evaluations of performance illustrate that the proposed protocol achieves better performance in terms of the bandwidth consumption, the number of signaling messages between the home network and the serving network, the computation cost and the storage cost in the serving network compared with several existing schemes. Copyright © 2013 John Wiley & Sons, Ltd.