In order to support multicast, efficient multicast routing is crucial. Many present multicast routing algorithms assume that every node in the network support multicast. But in real networks, some nodes may not support multicast, others may limit the number of multicast copies in order to ensure network speed. Thus, the multicast capability of each node is represented in this paper by a degree-constraint. A distributed degree- constrained multicast routing algorithm is proposed which has smaller time complexity and needs smaller number of messages than other existing algorithms.