Compared with the traditional half-duplex (HD) communications, full-duplex (FD) wireless communications can achieve high spectrum efficiency in the physical-layer. However, the high throughput of the data-link layer is also urgently needed, resorting to the efficient full-duplex medium access control (FD-MAC) protocol. In this paper, we propose the two-stage-contention based medium access control protocol for full-duplex wireless networks (TF-MAC) to optimise the throughput of FD wireless networks. First, we design a request to send (RTS)/full-duplex clear to send (FCTS)/clear to send (CTS) based handshaking mechanism. Then, the FD back-off algorithm is proposed to reduce the collisions for FD transmissions among all nodes. Finally, based on the two-dimensional Markov chain, we derive the closed-form expression for the throughput of FD wireless networks. The simulation results demonstrate the performance of our proposed TF-MAC protocol.