Simultaneous transmission and reception of data packets in Full-Duplex (FD) communication can theoretically double the system throughput. However, efficient self-interference mitigation and symbol detection at the receiver is required to realize the full potential of FD communication in practical scenarios. In this paper, we propose a constellation-based FD medium access control (MAC) protocol (C-FD) for wireless local area networks (WLAN). In the proposed C-FD MAC protocol, the node and Access Point (AP) can exchange packets simultaneously by transmitting the symbols and using different modulation schemes. The superimposed constellation diagram has been used to decode the symbols efficiently at both ends. The novel feature of the C-FD MAC protocol is that it does not require any complicated interference cancellation techniques. The analytical results for Symbol Error Rate (SER), Packet Error Rate (PER), and throughput have been derived for the symmetrical and asymmetrical FD link considering the additive white Gaussian noise (AWGN) with Rayleigh fading. The proposed C-FD MAC protocol achieves nearly twice the throughput compared to Half duplex (HD) communication without compromising the SER. The analytical results have been validated with extensive simulation.