As the success of P2P file sharing systems such as BitTorrent and eMule, P2P has become a promising technology to provide video streaming services over the Internet. The P2P technology is shown to be capable of significantly reducing the transmission overhead of video server. However, due to the dynamic nature of peers, a P2P streaming system suffers from bursty packet loss caused by peer departures. Furthermore, as the packet being forwarded peer by peer, the situation becomes worse and worse. This problem is recognized as packet loss accumulation problem. To overcome bursty packet loss and eliminate packet loss accumulation problems caused by peer departures in P2P streaming systems, a multi-source structure combining with a distributed FEC scheme for P2P streaming systems is proposed. In the proposed structure, each peer connects to multiple parents according to the pre-specified FEC packets ensemble and each parent forwards partial streaming packets to the peer. If one or few parents fail, other parents can still provide most of remaining part of streaming packets that can be used to recover the missing packets by using packet level FEC scheme. To evaluate the performance of P2P streaming systems using the proposed multi-source structure, we first propose a Continuous-Time Markov Chain to model the arrival/departure behavior of parents in P2P systems. Based on the Markov Chain, we further derived equations to calculate packet loss probabilities for both single-source and multi-source P2P systems. The mathematical analyses show how the packet loss accumulation occurs in P2P systems and how the proposed multi-source structure eliminates packet loss accumulation problem. In addition, simulations are conducted using NS2 to evaluate the proposed multi-source structure. Simulation results verify that the proposed multi-source structure combining with an appropriate FEC protection is capable of overcoming burst packet loss and eliminating packet loss accumulation problems. The simulation results also show that the proposed multi-source structure performs better than the single-source and the PROMISE/CollectCast P2P systems in terms of packet loss, end-to-end delay, and PSNR. A prototype system is implemented to conduct a real experiment over the Internet to validate the effectiveness of the proposed scheme.