In the distributed computing environments such as wireless network, the key exchange protocol with mutual authentication is critical to the following secure sessions between communicators and more attentions are paid to the provability of the protocol security. A mutual authentication key agreement protocol, MAKAP (mutual authenticated key agreement protocol) is proposed. The security of the protocol is proved in Bellare-Rogaway's model and its computation cost is also analyzed. MAKAP has advantages over other protocols in its security provability and only spends moderate computation cost, so it is quite practical.