In this paper, we formulate and realize a definition of security for three-party key distribution within the universally composable (UC) framework. That is, an appropriate ideal functionality that captures the basic security requirements of three-party key distribution is formulated. We show that UC definition of security for three-party key distribution protocol is strictly more stringent than a previous definition of security which is termed AKE-security. Finally, we present a real-life protocol that securely realizes the formulated ideal functionality with respect to non-adaptive adversaries.