As most proxy caches for streaming media cache only a part of the video, the most important issue for a caching algorithm is to determine which portion of the video should be cached. Due to different part of the video can have different popularity, the studying of the internal popularity characteristics of streaming videos is very important for the development of efficient cache mechanisms. In this paper, we showed that the internal popularity of the majority of the most popular videos obeys a ..-transformed Zipflike distribution through analyzing two 7-month long traces recorded at different streaming video servers of an entertainment video-on-demand provider. Based on this empirical internal popularity distribution model, we then proposed a new dynamical caching algorithm. The results of simulations proved that this algorithm can have better performance than algorithms based on other models. And it has similar performance compare with fine-grained caching but requires significantly less state information.