Password-based authenticated key schemes have a wide range of applications, especially the consumers who have no device capable of securely storing high entropy secret keys. The three-party password-based key exchange protocols using Weil pairing proposed by Wen is vulnerable to impersonation attack. By introducing hard artificial intelligence problem, the authors show an improved protocol, which can resist against not only the impersonation attack but also all the other well-known attacks. Analysis also shows that improved protocol reduces about one third computational costs and two thirds throughputs. The protocol is suitable for lightweight or mobile equipments.