To maintain the quality of multicast tree in supporting dynamic membership is critical important for the tree receivers. We propose an integrated approach that combines core migration with local search to afford the receivers a consistent quality service. The main ideas are always to migrate the core to the topological center of multicast tree within limited overhead and to provide multiple routes via local search for a new receiver to meet its quality requirements. Our algorithm aims to meet a predefined upper bound delay along path to individual receiver and satisfy the constraint of inter-destination delay variation among all receivers. In simulation results, it is shown that the proposed algorithm approximately provides the cost saving of 10%, the maximum delays of 25% and the inter-destination delay variation of 12%, compared to the existing approaches.