A multiple-input multiple-output two-way amplify-and-forward relay network with energy harvesting is considered in this paper. Under the transmit power constraints at sources and relay, a beamforming design problem is formulated, which minimizes the total mean square error while still guaranteeing sufficient energy harvested at the sources. Since this problem is nonconvex, an alternating optimization method based on generalized singular value decomposition (GSVD) is proposed and the algorithm is proved to be convergent. Moreover, based on the successive convex approximation, an iterative refinement is further designed to improve the solution quality of the GSVD scheme. Numerical results show good performance of the proposed schemes.