In this paper，we consider the transmitter beamformer design at relays for a full-duplex two-way relay system where the two sources are equipped with multiple antennas, and each one of the nearby relays is equipped with two antennas with one for transmission and the other for reception. Under the constraints of the limited transmit power and zero forcing nulling technique used at the relays, the proposed two algorithms are the linear relay beamformers that are respectively to iteratively: minimize the weighted mean square error of the two source nodes and maximize the smaller of signal to noise ratio of the two source nodes The effectiveness and efficiency of the proposed algorithms are evaluated by numerical experiments in terms of the weighted sum rate and the CPU running time.