The full-duplex technique can effectively increase the system throughput, which is beneficial for the application of IoT. However, the residual self-interference can not be ignored in the full-duplex relay system. In this paper, by considering the equivalent multipath signal with a long delay, the amplify-and-forward (AF) full-duplex relay system with zero-setting OFDM is proposed where an additional processing unit is added at the relay. The function of the processing unit is to change the amplification factor periodically. Theoretical analysis demonstrates that the proposed scheme can eliminate the equivalent inter-symbol interference (ISI) component of the residual self-interference. Furthermore, the closed-form expression of SINR gain is given by comparing the SINR of the proposed system and the traditional relay system. Meanwhile, the optimal amplification factor is also obtained using the gradient descent method.