While the overall bandwidth of peer-to-peer live video streaming system scales automatically as peers collectively contribute the bandwidth, each peer also demands to download at the specified video playback rate so as to play the video smoothly. Therefore, a fundamental problem arisen is how to balance the bandwidth supply and demand in the peer-to-peer system to enjoy peers with the best video quality. To address this problem, we propose a fully distributed peer-to-peer video streaming framework which automatically adapts the network towards full bandwidth utilization. Our design possesses two unique features. First, a special link-level homogenous overlay network is formed in which all the overlay links approach to have an identical bandwidth value. With such a feature, video flowing through the overlay links will not encounter any bottlenecks, and peers can thus achieve the guaranteed downloading rates. Second, based on the peer downloading rate observed locally at the streaming server, the server can adaptively adjust the video playback rate so that peers can achieve the best video quality with full bandwidth utilization. The effectiveness of our framework is verified through extensive simulations.