In recent years, mesh-pull peer-to-peer streaming systems are popular. However, the service providers of these systems have to pay high expense for the high consumption of servers’ bandwidth. Therefore, the research on providing better video quality with limited supply of bandwidth is very meaningful. However, there are few works focusing on this topic. In this paper, we analyzed the optimal throughput scheduling problem, and proposed a near optimal scheduling algorithm BBS and an effective heuristic MRBF, they eliminate or reduce scheduling waste significantly and get high throughput. The results of extensive simulations shows: our solution can provide better streaming quality or sustain higher streaming rate with limited supply of bandwidth than existing scheduling methods.