This paper presents and analyzes the performance of a weighted-window based cache replacement policy for the efficient media caching in streaming media cache servers. The proposed policy makes, for each cached object, use of the reference count, reference time, amount of media delivered to clients and, in particular, the periodic patterns of user requests. Also, by giving weights to the recently referenced media contents, the replacement policy adequately and swiftly reflects the ever-changing characteristics of users preferences. The simulation studies show that the performance of the proposed policy has improved over the conventional policies such as LRU, LFU and SEG - in terms of hit ratio, byte hit ratio, delayed start and cache input.