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Traditional IP multicast in a network domain is likely to imply a huge burden of storage and forwarding for routers and it's hard to support quality of service. The recent proposed application layer multicast is more scalable but increases traffic load and end-to-end delay. In the paper, we make multicast supporting comparable multi-class services on the overlay network comprising only edge routers. Considering resource limitation on the router and multi-class services by the member, the problem to build minimum cost trees is NP-hard, so we design three feasible heuristic algorithms to solve it. Extensive simulations are conducted to evaluate the performance of the proposed heuristics and validate the effectiveness of reducing the total tree cost and iteration times under considered constraints. The proposal is expected to combine with DiffServ or MPLS VPN networks to fulfill multi-class QoS multicast.