Wireless full-duplexing enables a transmission and a reception on the same frequency channel at the same time, and has the potential to improve the end-to-end throughput of wireless multi-hop networks. In the present paper, we propose a media access control (MAC) protocol for wireless full-duplex and multi-hop networks called Relay Full-Duplex MAC (RFD-MAC). The RFD-MAC is an asynchronous full-duplex MAC protocol, which consists of a primary transmission and a secondary transmission. The RFD-MAC increases the full-duplex links by overhearing frames, which include 1-bit information concerning the existence of a successive frame, and selecting a secondary transmission node using the gathered information. The gathered information is also used to avoid a collision between the primary and secondary transmission. Simulation results reveal that the proposed RFD-MAC improves up to 68%, 49% and 56% of end-to-end throughput compared to CSMA/CA, FD-MAC and MFD-MAC, respectively.