To establish secure channel for network communication in open and distributed environments, authenticated key agreement protocol is an important primitive for establishing session key. So far, a great deals of identity-based protocols have been proposed to provide secure mutual authentication and common session key establishment in two-party setting for secure communications in the open environment. Majority of the existing authenticated key agreement protocols only provide partial forward secrecy. Therefore, such protocols are unsuitable for real-world applications that require a stronger sense of perfect for- ward secrecy. In this paper, we present a secure two- party identity-based authenticated key agreement protocol with achieves most of the required security attributes. We also show that the scheme achieves the security at- tributes include known-key secrecy, perfect forward secrecy, PKG forward secrecy, key-compromise impersonation resilience, unknown key-share resilience, no key revelation and known session-specific temporary key information secrecy and also proposed algorithm achieves the shorter run time, lower computation cost, lower communication cost, and a more effective storage method. In addition, the adversary can not compromise the agreed session key.