A method of providing a quality-guaranteed service on a converged network and a network apparatus using the method are provided. The method includes: receiving a request of a quality-guaranteed service from a user terminal and providing information on the service quality of at least one adjacent network apparatus; receiving service information, including service-quality-information selected by the user terminal in the provided service-quality-information and content information, from the user terminal and transmitting the service information and a traffic-collection-start message to an adjacent network apparatus providing the selected service-quality-information; and transferring a traffic stream received from the adjacent network apparatus, to the user terminal. According to the method and apparatus, a quality-guaranteed service can be provided through a converged network.