The aim of this study is to forecast the number of free-riders in P2P networks which can help network managers to know the status of the networks in advance and take appropriate measures to cope with free-riding behavior. Free-riding behavior is common in P2P networks, which has a negative impact on the robustness, availability and stability of the networks. Severe free-riding behavior may lead to the crash of the whole P2P application system. Based on the research of free-riding behavior in P2P networks, this paper constructs a free-rider forecasting model (GST model) using Gray System Theory. Simulation experiments show that this model has high feasibility, and can carry out reasonable predictions on the number of free-riders in P2P networks.