In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed algorithm is energy-efficient which is more applicable to the future green network. It considers both the sum-MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition(OCD) method, the energy-efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers(ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance. In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed It is both more sum to MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition (OCD) method, the energy efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers (ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance.