Most peer-to-peer live multimedia streaming systems either rely on an overlay infrastructure to deliver media data or request participating peers to search and fetch their demanded data without relying on a dedicated overlay structure. While the former approach, namely the infrastructure-centric approach, may require sophisticated construction and maintenance for an overlay network with good quality, the latter, called the infrastructure-less approach, may take significant overheads in searching and caching the demanded contents. In this paper, we propose a hybrid design that takes both advantages of the infrastructure-centric and infrastructure-less approaches. The performance of our design is efficient and mathematically provable. The simulation results also confirm the efficiency of our design.