The requirement for real-time multimedia communications raises challenges for constructing multicast trees with multiple Quality of Service (QoS) parameters, for example, bandwidth, delay, delay jitter, error rates, and so on. In this paper, we present a new method for establishing multicast trees with multiple QoS parameters based on data envelopment analysis techniques. We first apply data envelopment analysis techniques for evaluating the relative efficiency of arcs in the presence of QoS parameters. Then, an integer linear programming model based on the relative efficiency of arcs is proposed to obtain multicast trees for transmitting data from a source to each destination. The proposed approach is illustrated and evaluated through numerical examples.