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With the popularity of wireless communication, the security of mobile networks becomes more and more important. However, due to the computation limitation, many existing authentication key agreement protocols are not suitable for wireless mobile networks. In 2005, Sui et al. proposed an efficient authentication key agreement protocol, but their protocol can not resist the off-line password guessing attack. Therefore, Lu et al. present an enhanced authentication key agreement protocol to against this attack. However, we find that their protocol can not withstand the parallel guessing attack. Here, we propose an improved authentication key agreement protocol based on elliptic curve for wireless mobile networks that can enhance the security of A- Key distribution protocol in 3GPP2.