Abstract: Most of the study on the beamforming design for Two-Way Relaying Network (TWRN) is based on the reciprocity assumption. Assuming channel is nonreciprocal, this paper designs the beamforming coefficients to maximize the sum-rate of the network subject to the Total Relay Power Constraint (TRPC). To solve this nonconvex problem, a branch-and-bound based algorithm is firstly proposed and the global optimum is proved to be obtained. Secondly, a suboptimal algorithm is proposed. This algorithm assumes the suboptimal solution is the linear combination of two known vector, thus only two real variables need to be optimized, which requires low complexity. Simulation results show that the branch-and-bound algorithm performs better than other existing algorithm. The suboptimal algorithm suffers performance loss compared to the optimal solution, but outperforms other algorithm when the number of relay nodes is relatively small or the average power of relay is relatively small.