Due to the difficulties in deployment of IP multicast, the overlay multicast networks (OMN) are being increasingly recognized as a viable alternative to construct a general multicast service infrastructure. To settle the heterogeneity of bandwidth required by real-time multimedia application, the multicast routing problem in heterogeneous OMN is discussed. A new network model of heterogeneous OMN is described by extending the degree-constrained model. Adopting the strategy of layered bandwidth allocation, a heuristic routing algorithm, called layered compact tree (LCT) is proposed to build a minimum delay radius multicast tree in heterogeneous OMN. The properties of LCT are also proved and analyzed in theory. The simulation results show that LCT could reduce both hops and network resource usage of the tree effectively, and keep a little increase in delay radius while the allocated bandwidth decreases.