To enhance the throughput of wireless local area networks (WLANs) by efficiently utilizing the radio resource, a distributed coordination function-based (DCF-based) orthogonal frequency division multiple access (OFDMA) WLAN system has been proposed. In the system, since each OFDMA sub-channel is assigned to the associated station with the highest channel gain, the transmission rate of DATA frames can be enhanced thanks to multi-user diversity. However, the optimum allocation of OFDMA sub-channels requires the estimation of channel state information (CSI) of all associated stations, and this incurs excessive signaling overhead. As the number of associated stations increases, the signaling overhead severely degrades the throughput of DCF-based OFDMA WLAN. To reduce the signaling overhead while obtaining a sufficient diversity gain, this paper proposes a channel access scheme that performs multiple DCF-based channel access. The key idea of the proposed scheme is to introduce additional DCF-based prioritized access along with the traditional DCF-based random access. In the additional DCF-based prioritized access, by dynamically adjusting contention window size according to the CSI of each station, only the stations with better channel state inform their CSI to the access point (AP), and the signaling overhead can be reduced while maintaining high multi-user diversity gain. Numerical results confirm that the proposed channel access scheme enhances the throughput of OFDMA WLAN.