Application level multicast approaches have attracted interests in both research and industrial communities. Among various approaches, constructing the overlay multicast tree based on mesh network is very promising for a large multicast group size. This approach is efficient in bandwidth utilization but suffer from high computation overhead. In this paper, we present a new approach for constructing an overlay multicast tree in a large scale media streaming system using neural networks. The media server first constructs an overlay multicast tree for requests arriving in a relatively short time interval. Then the subsequent requests can join the multicast tree in a distributed way. To utilize the interface bandwidth efficiently, we formulate the original tree construction problem as a balanced multicast tree problem and propose a new SOFM-like neural network algorithm to obtain the solution. For the requests arriving at a later time, the proxy servers process the requests and join the multicast tree using a decentralized prediction based on a multilayered neural network. The tree is kept balanced in the tree joining process by having proxy servers predict the traffic load on its neighbors.