In this letter, we introduce quality of service-aware beamformer design for full-duplex wireless-powered relay with self-energy recycling. In the first phase of communication, the information signal is transmitted from the source to the relay. In the second phase, the relay forwards this signal using beamforming while it harvests energy via self recycling and from the source. The aim is to satisfy the signal-to-noise ratio requirement of the destination with minimum transmission power from the relay's own battery. A closed-form solution for the optimum relay beamformer is derived and the feasibility conditions are obtained. The effects of different system parameters on the relay's performance are discussed in the simulation results.