Wireless Full-Duplex (FD) communication can double the point-to-point throughput. To obtain the full benefits of the FD technique in multi-hop networks, its potential throughput performance in multi-hop networks should be clarified qualitatively and quantitatively. Developing an analytical model for FD multi-hop networks is effective and useful for not only clarifying such network dynamics but also developing the optimal protocol design. However, generalized analytical expression for the end-to-end throughput of FD multi-hop networks has not been proposed. This paper proposes analytical expressions for the end-to-end throughput of string-topology wireless FD multi-hop networks. Our approach is to integrate with the analytical model of the airtime expression, which is an effective analytical approach of the throughput analysis for Half-Duplex (HD) multi-hop networks, and the Markov-chain model considering the FD MAC operation. The proposed model clarify the detailed effect of the FD MAC operation on the throughput performance in multi-hop networks. In particular, it can obtain the end-to-end throughput of FD multi-hop networks for arbitrary number of hops, arbitrary payload size and arbitrary value of the minimum contention window. The analytical expressions verified by comparisons with the simulation results. From the comparisons with the results in HD multi-hop networks, we confirm the effectiveness of the FD communication in multi-hop networks.