The efficient distribution of stored information has become a major concern in the Internet. Since the web workload characteristics show that more than 60% of network traffic is caused by image documents, how to efficiently distribute image documents from servers to end clients is an important issue. Proxy cache is an efficient solution to reduce network traffic. And it has been shown that an image caching method (Graceful Caching) based on hierarchical coding format performs better than conventional caching schemes in recent years. However, as the capacity of the cache is limited, how to efficiently allocate the cache memory to achieve a minimum expected delay time is still a problem to be resolved. This paper presents an integrated caching algorithm to deal with the above problem for image databases, web browsers, proxies and other similar applications in the Internet. By analyzing the web request distribution of the Graceful Caching, both replacing and pre-fetching algorithms are proposed. We also show that our proposal can be carried out based on information readily available in the proxy server; it flexibly adapts its parameters to the hit rates and access pattern of users' requesting documents in the Graceful Caching. Finally we verify the performance of this algorithm by simulations.