Peer-to-peer streaming has recently gained attention as an effective solution to support large scale media streaming applications over the Internet. One of the main challenges of peer-to-peer video streaming is the cumulative impact of the Internet packet loss due to the decoding dependency of the compressed video frames. In this paper we study the impact of the Internet packet loss on the performance of peer-to-peer video streaming systems, and analyze the efficiency of various packet loss recovery policies in such systems. Our analytical and simulation results show how the Internet packet loss can affect the performance of peer- to-peer video streaming systems and how different packet loss recovery policies can be effective for such systems. Our analysis results give us some insights that can be used in designing efficient peer-to-peer video streaming systems.