P2P streaming technology has advantages of scalability and availability comparing to the popular IP multicast. This paper proposes an approach to apply the P2P streaming technology to the delay-sensitive multimedia multicast applications. In order for the P2P streaming to be applied to the delay-sensitive applications, prior construction of delay-guaranteed overlay network is necessarily required. Moreover, the delay-guaranteed overlay network should be able to be kept even when the hand-overs occur owing to the departures of the intermediate P2P peers. This paper proposes a delay-guaranteed overlay network construction method by using the bandwidth and end-to-end delay based admission control and the backup peer based hand-over control mechanism.