The proxy mechanisms widely used in WWW systems offer low-delay data delivery by a means of ``proxy server''. By applying the proxy mechanism to the video transfer, we expect a real-time and interactive video streaming without introducing extra load on the system. In addition, if the proxy appropriately adjusts the quality of cached video data to the user's demand, video streams can be delivered to users considering their heterogeneous QoS requirements. In this paper, we propose proxy caching mechanisms that can achieve a high-quality video transfer considering the user's demand and the available bandwidth. In our system, a video stream is divided into pieces. The proxy caches them in local buffer, adjusts their quality if necessary, transmits them to users, replaces them with cached data, and retrieves them from the video server, considering user's requirement. We evaluate the proposed video caching mechanisms and compare their performance in terms of the required buffer size, the play-out delay and the video quality. Consequently, the validity of the video quality adjustment in the proxy is confirmed.