Full-duplex transmission is a promising technique to enhance the capacity of communication systems. In this paper, we investigate two-way amplify-and-forward (AF) relay systems in the full-duplex scenario. Compared with the traditional half-duplex AF relaying, the full-duplex system uses only a single phase to complete the two-way or bidirectional transmission and has the potential to achieve higher spectral efficiency. In order to further improve the system performance, the transmit power is optimized among the source nodes and the relay node. Numerical results are provided to compare the performance of the full-duplex system and the half-duplex system in terms of the average achievable rate. The effect of residual self-interference introduced by full-duplex radios and the benefits of transmit power optimization are also illustrated.