For the simultaneous wireless information and power transfer(SWIPT), the full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean-square-error(MSE) criterion, the optimization problem of joint transceiver design with transmitting power constraint and energy harvesting constraint is formulated. Next, by semidefinite relaxation(SDR) and randomization method, the SDRbased scheme is proposed. In order to reduce the complexity, the closed-form scheme is presented with some simplified measures. Robust beamforming is then studied considering the practical condition. The simulation results such as MSE versus signal-noise-ratio(SNR), MSE versus the iteration number, well prove the performance of the proposed schemes for the system model. The full-duplex MIMO system can achieve simultaneous transmission of information and energy more efficiently than the half-duplex. Based on the mean-square-error (MSE) criterion, the optimization problem of the coupling scheme of transmitting power constraint and energy harvesting constraint is formulated. Next, by semidefinite relaxation (SDR) and randomization method, the SDR-based scheme is proposed. The simulation results such as MSE versus signal-noise-ratio (SNR), MSE versus the iteration number, well prove the performance of the proposed schemes for the system model.