The large-scale multiple-input multiple-output system with full-duplex relay is a promising candidate for future mobile communication systems, where accurate channel estimation is very challenging due to interference. In this paper, we address two channel estimation problems for such systems: individual estimation, where both the base station (BS) and the relay estimate their respective channels, and cascaded estimation, where only the BS estimates the cascaded two-hop channel. For the BS, we propose an estimator that exploits the sparsity and slowly varying nature of the channel in the beam domain. Then, we analyze the probability of correctly distinguishing the desired and interfering direct-link channels. For the relay, we present an estimator that simultaneously estimates both the source-to-relay and self-interference channels based on the expectation-maximization algorithm. The performance of this estimator is also analyzed. Numerical results demonstrate the excellent performance of the proposed channel estimators and corroborate the analysis results.