This paper identifies that time variance behavior (TVB) exists in today's Web proxy systems where the user request profile varies with time. As future video on demand (VoD) systems will very likely be implemented on the Internet, it is expected that TVB will have a significant impact on the performance of the video caching servers such as CDN. In this paper, a TVB-aware prefetch algorithm is proposed. Simulations on a distributed video system show that TVB-aware prefetch algorithm performs much better than conventional prefetch algorithm even when the user request patterns are not fully known.