The purpose of the multiple key agreement protocol is to get efficiency in computational and communicational aspects compared to multiple executions of single key agreement protocol. However ID based tripartite multiple key agreement protocols have been proposed, it is reported that they can not resist unknown key-share attack or impersonation attack. How to design a secure and efficient ID-based authenticated tripartite multiple key agreement scheme to prevent all kinds of attacks remains an open problem. This paper proposes a multiple key agreement scheme combing the existing single key agreement protocol with a key derivation function. The proposed scheme can not only increase computational efficiency compared to the existing multiple key agreement protocol, but can ensure security of the proposed schemes by using a security proofed single key agreement protocol and key derivation function.