This paper presents a novel data organizing and delivery framework for P2P media streaming which is aware of media content. In this framework, the media data is partitioned GOP by GOP, and reorganized according to the frame-priorities within a GOP. All GOPs cached in the media buffer of a peer node can be scheduled concurrently, while the frames contained in each GOP are transmitted by order strictly according to their priorities. Analysis and primary experimental results show that the proposed techniques can provide not only self-adaptive QoS for heterogeneous network conditions, but also quick channel switching with near fixed delay time.