This paper describes a modeling of service composition manager based on TINA (Telecommunication Information Networking Architecture). The Service composition function is mainly motivated by the desire to easily generate new service using existing services from retailers or $3^{rd}$-party service providers. The TINA-C specification for the service composition does not include the detailed composition procedure and its object models. In this paper, we propose a model of components for the service composition, which adapts a static composition feature in a single provider domain. To validate the proposed modeling, we implemented prototype service composition function, which combines two multimedia services; a VOD service and a VCS service. As a result, we obtain the specification of the detailed composition architecture between a retailer domain and a $3^{rd}$-party service provider domain.