Key agreement protocols are designed so that two or more entities can establish a session key in order to communicate with confidentiality over an open network or to achieve a cryptographic goal such as data integrity. Till date, no (secure) tripartite key agreement protocol could provide authentication for entities without introducing certifications into the protocol or combining the protocol with a digital signature scheme. In addition, at least one-round of data transmission has been required for the current protocols. In this paper, we propose an ID-based tripartite key agreement protocol which is non-interactive. This scheme is secure against a collusion of a maximum of k entities. We also show how this protocol can be modified into an one-round tripartite key agreement protocol so that different session keys can be established in each run of the protocol.