The 3GPP is investigating the concept of integrated access and backhaul (IAB) to provide high capacity wireless backhaul for 5G network. In this paper, we present an analysis of ergodic capacity for full-duplex IAB system, where full-duplex is introduced to further improve the ergodic capacity. Two kinds of interference are considered: the backward interference between two adjacent base stations and the residual self-interference introduced by full-duplex. We derive a closed-form solution of ergodic capacity by exploiting the probability density function of the end-to-end signal-to-interference-plus-noise ratio, and extend this derivation from three-hop system to arbitrary K-hop system. Simulation results are further provided to demonstrate the validity of the proposed mathematical analysis, and show an obvious advantage over half-duplex IAB system.