Many multimedia group applications require the construction of multicast tree satisfying the quality of service (QoS) requirements. To support real time communication, computer networks need to optimize the Delay and Delay-Variation Bounded Multicast Tree (DVBMT). The problem is to satisfy the end-to-end delay and delay-variation within an upper bound. The DVBMT problem is known to be NP complete. In this paper, we propose an efficient core selection algorithm for satisfying the end-to-end delay and delay-variation within an upper bound. The efficiency of the proposed algorithm is validated through the simulation. The simulation results reveal that our algorithm performs better than the existing heuristic algorithms.