In 2000, Joux proposed a one-round protocol for tripartite Diffie-Hellman. In 2003, Shim presented an efficient one-round tripartite authenticated key agreement protocol based on Weil pairing to resist the man-in-the-middle attack appears in Joux’ s. In this paper, we show that Shim’ s protocol still cannot withstand the insider attack and the keycompromise impersonation attack. We propose a secure one-round tripartite authenticated key agreement protocol to solve the existed problems.