In this letter, we propose a novel channel access scheme based on non-orthogonal multiple access (NOMA) for IEEE 802.11 to improve the throughput performance and connectivity of wireless local area network (WLAN). We consider a wireless network with NOMA at the physical layer and distributed coordination function (DCF) in the medium access control (MAC) layer. The proposed scheme allows the simultaneous transmission of multiple nodes using NOMA as well as reduces the number of contending nodes. In addition, we present a simple yet accurate analytical model for NOMA based IEEE 802.11 multi-rate WLAN. The analytical findings show that the aggregate throughput and connectivity are significantly improved compared with conventional IEEE 802.11multi-rate WLANs. The analytical results are corroborated with extensive simulation studies.