Recently, owing to the advances in the self-interference cancellation technology, the in-band full-duplex (FD) capability has been demonstrated at Wi-Fi range. However, the simultaneous uplink (UL) and downlink (DL) transmission may lead to inter-user interference (IUI) and result in decoding failure. Spectrum efficiency should also be considered in the construction process of the FD transmission. In this paper, we propose a hybrid half-duplex/FD MAC protocol based on a two-fold RTS/CTS contention resolution mechanism, in order to fully exploit the channel access opportunities provided by the simultaneous UL and DL transmissions. The noteworthy features of the proposed protocol lie in the following two aspects. First, the protocol provides the flexibility for the AP to decide the probability of constructing FD transmission, and then it adopts a second-fold of RTS/CTS mechanism to prevent the constructed transmission from being affected by the IUI. The second-fold contention and the probability of constructing FD transmission are optimized separately to maximize the spectrum efficiency given different transmission demands. Simulation results show that the proposed MAC protocol achieves higher capacity compared with previous works, and the hybrid characteristic enables the FD Wi-Fi networks to meet with different system requirements.