In this paper, the two-way full-duplex Gaussian channel (TW-FD-GC) is revisited by considering Gaussian state interference non-causally known by the corresponding transmitter, which is also called the two-way full-duplex dirty paper channel (TW-FD-DPC). We propose a novel coding scheme for the TW-FD-DPC, which perfectly eliminates the effect of the state interference. Numerical result shows that for a fixed decoding error probability, the encoding-decoding complexity of this scheme is extremely low.