The fundamental challenges for full-duplex (FD) relay networks are the self-interference cancellation (SIC) and the cooperative transmission design at the relay. This paper presents a practical amplify-and-forward (AF) FD one-way relay scheme for orthogonal frequency division multiplexing (OFDM) transmission with multi-domain SIC. It is found that the residual self-interference (SI) signals at the relay can be regarded as an equivalent multipath model. The effects of the residual SI at the relay are incorporated into the equivalent end-to-end channel model, and the inter-block interference can be removed at the destination by using cyclic prefix (CP) protection. Based on the equivalent multipath model, we present a solution for optimizing the amplification factor on the performance of signal-to-interference-plus-noise ratio (SINR) when the equivalent multipath length is longer than the CP. Furthermore, a practical one way FD relay network with 3 nodes is built and measured. The simulation and measured results verify the superior performance of the proposed scheme.