In this paper we explore the use of full-duplex radio to improve the spectrum efficiency in a two-way relay channel where two sources exchange information through an multi-antenna relay, and all nodes work in the full-duplex mode. The full-duplex operation can reduce the overall communication to only one phase but suffers from the self-interference. Instead of purely suppressing the self-interference, we aim to maximize the end-to-end performance by jointly optimizing the beamforming matrix at the relay which uses the amplify-and-forward protocol as well as the power control at the sources. To be specific, we propose iterative algorithms and 1-D search to solve two problems: finding the achievable rate region and maximizing the sum rate. At each iteration, either the analytical solution or convex formulation is obtained. We compare the proposed full-duplex two-way relaying with the conventional half-duplex two-way relaying, a full-duplex one-way relaying and a performance upper bound. Numerical results show that the proposed full-duplex scheme significantly improves the achievable data rates over the conventional scheme.