This study considers the problem of beamforming optimisation in an amplify-and-forward relaying cooperative network, in which the relay node harvests the energy from the radio-frequency signal. Based on the self-energy recycling relay protocol, the authors study the beamforming optimisation problem. The formulated problem aims to maximise the achievable rate subject to the available transmitted power at the relay node. The authors develop a semidefinite programming (SDP) relaxation method to solve the proposed problem. They also use SDP and the full search to solve the beamforming optimisation based on a time-switching relaying protocol as a benchmark. The simulation results are presented to verify that the self-energy recycling protocol achieves a significant rate gain compared with the timeswitching relaying protocol and the power-splitting relaying protocol.