In this paper, an iterative design method for beamformers is proposed for multiple-input multiple-output (MIMO) two-way relay networks with multiple pairs of source nodes. It is known that the joint beamformer design problem based on the minimum mean-square-error (MMSE) is known to be nonconvex, and it cannot be analytically solved. To manage this difficulty, a novel iterative algorithm is proposed, which uses duality relationships. First, the MSE duality for MIMO two-way relay networks with multiple pairs of nodes is presented. Moreover, the optimization problem is divided into three subproblems, which can be separately solved; then, the duality is applied to the proposed iterative algorithm, which provides closed-form solutions for all subproblems. The numerical results demonstrate that the proposed method improves network performance and can be applied to various communication systems that use the two-way relay network.