In a dense wireless network, concurrent transmissions normally increase interference and reduce network performance. In such an environment, however, there is a possibility that a frame can be decoded correctly if its receive power is higher than that of another frame by some predefined value (i.e., the so-called capture effect). As a result, the unfairness of throughputs among network nodes likely occurs in that context. This research aims to quantify the throughput performance of only one access point Wireless Local Area Networks (WLANs) with dense network nodes in the presence of the capture effect. We first propose a new analytical model, which can express not only WLANs' throughputs but also WLANs' unfairness transmission. The validity of the proposed model is confirmed by simulation results. Second, relying on the model, we present a novel Medium Access Control (MAC) protocol-based solution, which realizes throughput fairness between network nodes induced by the capture effect.