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To support large-scale live Internet broadcasting services in the content delivery networks (CDNs) efficiently, we consider a cost-effective multicast approach among the CDN servers in the backbone. This way, the access bandwidth demand can be reduced. The problem is to optimize routing paths among the service nodes in the multicast overlay backbone, and it has been proved to be NP-Hard. We will minimize the accumulative weighted latency from the source to the service nodes according to the number of clients served by each service node. We proposed an algorithm to optimize the multicast tree directly different from the traditional solutions to find paths and integrate them into a multicast tree. Simulation results showed that our algorithm performs well in seeking, converging speed and adaptability scale.