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This paper investigates the secrecy performance of full-duplex relay (FDR) networks. The resulting analysis shows that FDR networks have better secrecy performance than half duplex relay networks, if the self-interference can be well suppressed. We also propose a full duplex jamming relay network, in which the relay node transmits jamming signals while receiving the data from the source. While the full duplex jamming scheme has the same data rate as the half duplex scheme, the secrecy performance can be significantly improved, making it an attractive scheme when the network secrecy is a primary concern. A mathematic model is developed to analyze secrecy outage probabilities for the half duplex, the full duplex and full duplex jamming schemes, and the simulation results are also presented to verify the analysis.