Abstract: Efficient multicast functionality satisfying QoS constraints is fundamental to modern computer networks, especially for such applications as video conferencing systems, multimedia education systems, video on demand, and auction on networks. In this paper, a accelerating weighted cost algorithm is presented. It accelerates the increase of the weighted cost according to the accumulated delay on the passed path and the remained delay. It can find sub-optimal cost multicast tree meeting delay-constraint, suitable for real-time and communications. It can dynamically modify the tree to adapt the changes of destinations. It also overcomes the shortcomings of the traditional algorithms which deal with the cost and delay separately and need a lot of retrospect.