In this work, we propose a full-duplex relay (FDR) network for secure communication in the presence of an eavesdropper. We consider both the destination and the amplify-and-forward relay has a full-duplex capability for a higher rate and/or a stronger secrecy performance. In particular, the destination transmits a cooperative jamming signal while receiving the relayed signal. To get analytic understanding, we derive a closed form expression for the secrecy rate of the proposed FDR network. Numerical evaluations arc also conducted to verify the analytic results.