In the telecommunications network, multicasting is widely used recently. Multicast tree problem is modeled as the NP-complete Steiner problem in the networks. In this paper, we study algorithms for finding efficient multicast trees with hop and node degree constraints. Multimedia service is an application of multicasting and it is required to transfer a large volume of multimedia data with QoS(Quality of Service). Though heuristics for solving the multicast tree problems with one constraint have been studied. however, there is no optimum algorithm that finds an optimum multicast tree with hop and node degree constraints up to now. In this paper, an approach for finding an efficient multicast tree that satisfies hop and node degree constraints is presented and the experimental results explain how the hop and node degree constraints affect to the total cost of a multicast tree.