This paper presents a cache scheme for image databases, web browsers, proxies and other similar applications in Internet. The current cache system employs a hard strategy: either the image is stored in a cache or not even its data is quite big. We have proposed a caching scheme featuring human memory mechanism (image database system featuring graceful oblivion), which is called Graceful Caching. The previous work shows that Graceful Caching reduces user response time by assigning a variable amount of memory to each image. Several recent studies suggest that prefetching techniques could be employed to further improve the cache performance, by anticipating and prefetching future client requests. Some approaches based on request frequency have been proposed to the conventional caching (hard system) and got better results. In this paper, we try to apply a request frequency-based approach to Graceful Caching system, in which a progressive image format is used. Based on the analysis of web request probability in Graceful Caching, we go on to propose a new prefetching algorithm that drastically improves cache performance of system. We verify the performance of this algorithm by simulations.