In this paper, we investigate the sum rate of full-duplex (FD) two-way massive MIMO amplify-and-forward (AF) relay system with channel aging, where minimum mean-square-error (MMSE) technique is applied into channel estimation and maximum ratio combining/maximum ratio transmission (MRC/MRT) is adopted at the relay. In contrast with prior literature, the consideration of both the spatial antenna correlation and the time correlation of channel aging makes the corresponding performance analysis more challenging. The asymptotic results of the instantaneous sum-rate is derived in closed-form by using deterministic equivalent and it is proved that the instantaneous sum-rate is an increasing function of time correlation coefficient of channel aging and the antenna spatial correlation has a negative effect on the system performance. Finally, the analytical results are demonstrated through numerical analysis.