This paper presents a hybrid push/pull streaming scheme to take advantage of both the interval caching-based push method and the mesh-based pull method. When a new peer joins, a mesh-based pull method is adopted to avoid the overhead to reorganize the structure only if all of its potential preceding peers are likely to leave before the end of its playback. Otherwise, an interval caching-based push method is adopted so that the better performance of the push method can be maintained until it completes the playback. We demonstrate that our proposed scheme outperforms compared with when either the interval caching-based push method or mesh-based pull method is employed alone.