This paper considers a multi-user large-scale multiple-input multiple-output (MIMO) system with single cell working in full-duplex mode. Maximum ratio combining/maximum ratio transmission (MRC/MRT) is applied to maximize the output signal to noise ratio (SNR) of the receiver. Then we deduce the asymptotic uplink and downlink sum rate in full-duplex mode by using the large number theorem, also giving the comparison of traditional half-duplex and full-duplex. Besides, we analyze the influence of Doppler shift on the performance of the system. Finally, the change of the system performance on the user velocity is illustrated.