Deng, et al. proposed a security-provable mutually authenticated key agreement protocol MAKAP for mobile communication in 2003. This paper demonstrates by mounting an effective attack against MAKAP that the protocol has security flaws. It is vulnerable against unknown key-share attack. This paper investigates the reasons why such flaws exist and proposes an improved protocol version (called MAKAP-I protocol). The MAKAP-I protocol is not only provably secure within the random oracle model but also more efficient and practical in terms of computation and communication cost memory requirement and implementation cost, than the original MAKAP protocol.