In this modern era, the need for key agreement protocols equipped with high-speed Internet has become necessary in information/network security. An authenticated key agreement (AKA) protocol is a technique that negotiates a secret session key among various users in a network and is used in many scenarios like mutual authentication, data integrity, and many more. The current state-of-the-art include many AKA protocols that are either vulnerable to different attacks or incur massive communication and computational costs. This paper proposes an identity-based three-party authenticated key agreement (ID-3PAKA) protocol using elliptic curve cryptography (ECC). The proposed ID-3PAKA protocol generates a shared secret session key among three users. The security of the proposed ID-3PAKA protocol relies on the hardness assumption of the ECDLP and the CDH problems. The proposed ID-3PAKA protocol is safe against active and passive attacks, which is proved through the simulation of the OFMC and Cl-AtS back-ends of the AVISPA tool.