This paper studied two-party authenticated agreement protocol in the certificateless public setting.Analyzed the security of Liu-xu's certificateless authenticated two-party key agreement protocol,and it was shown that the scheme did not achieve strong security.The scheme was vulnerable to key compromise impersonation attack and leakage of ephemeral secrets attack.The reason why the attack can work was analyzed and proposed an improved scheme to remove the attack.It is not hard to devise certificateless authenticated two-party key agreement protocols that look secure,but making the proofs word is not always so simple.