The rapid evolution of real-time multimedia applications requires the multicast routing in underlying communication networks. Multicast aims at sending information from one or more sources to a set of destinations in the network. A multicast tree is the required solution for the multicast routing problem. On the other hand, the multimedia applications including video conferencing, interactive distributed games and video and audio on demand have a wide diversity of Quality of Service (QoS) requirements for traffic, including the cost, bandwidth, end-to-end delay, delay jitter, packet loss ratio and hop count, and etc. So, the real-time multimedia applications have been stimulating the demand for QoS based multicast routing in the computer communication networks. QoS multicast routing is an important technique to support data transmission in computer networks. Solution to the QoS multicast routing problem is to build a multicast tree, which spans from the source node to all destinations and satisfies certain QoS requirements. The main goals of QoS multicast routing are to efficiently allocate network resources and provide adequate QoS guarantees for end users of multimedia applications. On the other word, given a network, a source node and a set of destinations, the problem of routing on a multicast network can be quantified using several objectives, or metrics such as delay minimization, congestion minimization and cost minimization. A common objective is simply to minimize the costs associated with the connections used to route packets, that is, minimizing the total cost of the routing tree. The resulting problem is known as minimum cost multicast routing. In this case, the optimization goal can be proved to be equivalent to the minimum Steiner tree, a ltr" Keywords: Multicast routing, Quality of service, Steiner tree, Ants colony, Scalability