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This correspondence paper studies joint beamforming optimization and time allocation for a wireless powered two-way hybrid-relay network. As a general relaying architecture accommodating the existing relaying architectures in the literature as two special cases, we consider the two-way communication system where both energy-harvesting (EH) relays and non-EH relays exist. We aim to maximize the minimum rate by jointly optimizing the distributed beamforming vector at the relays, the energy beamforming matrix at the non-EH relays, and the EH time allocation with the energy constraints at the relays. The formulated problem is intractable to solve because the objective function and the energy constraints are highly nonconvex. We solve the optimization problem using the successive convex approximation. Simulations demonstrate that the proposed iterative algorithm considerably outperforms any existing approaches. [ABSTRACT FROM AUTHOR]