The Internet has enabled the dissemination and access of vast amounts of information to be easy. But dramatic increases of the number of users of Internet cause server overload, network congestion and client perceived latency. In addition, currently the number of continuous media data such as audio and video is growing rapidly on the Internet. In this paper, we propose a proxy caching scheme that stores a portion of continuous media stream or entire stream on the Internet. The proposed scheme reduces client initial latency and maximizes the amount of data served directly from cache without accessing the remote server. By caching the initial fraction of stream data, service startup latency can be reduced. And, by varying the size of the fraction of stream to be cached according to variation of stream popularity, we can utilize the cache space efficiently and maximize the amount of data served directly from cache. We use the caching utility of each stream for cache replacement. Caching ...