In multimedia new service on the internet, there are problems such as server overload, network congestion and initial latency. To overcome these problems, we propose a proxy push-caching scheme that stores a portion of continuous media stream or entire stream, and a transmission scheme of NOD continuous media, RTP-RR and RTP-nR to exploit push-caching scheme. With the proposed push-caching scheme, NOD server pushes fixed portion of stream to a proxy when new data is generated, and the cached size of each stream changes dynamically according to the caching utility value of each stream. As a result, the initial latency of client side could be reduced and the amount of data transmitted fro ma proxy server to client could be increased. Moreover, we estimate a caching utility value of each stream using correlation between disk space occupied by the stream and the amount of data stream requested by client. And we applied the caching utility value ot replacement policies. The performance of the proxy push-caching and continuous media transmission schemes proposed were compared with other schemes using simulations. In the simulation, these schemes show better results than other schemes in terms of BHR (Byte Hit Rate), initial latency, the number of replacement and packet loss rate.