In this paper, we have analyzed the performance of a BRAM (The Broadcasting Recognizing Access Method) protocol, as a CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) scheme, which is widely used in wireles LAN systems. We have selected a Fair BRAM protocol among CSMA/CA schemes, considering the fairness of channel usage and the simplicity of the protocol. We have compared the performance of BRAM protocol to that of CSMA/CD. to research the characteristics of BRAM in wireless LAN system. In order to analyze the performance of this system, we have set up an imbedded Markov chain and calculated state transition probabilities. Then we have calculated steady state probabilities and finally derived the throughput of a Fair BRAM moder. To verify our analysis, we have simulated practical models. Then, we have found that analytic results are very close to simulation ones. Our analysis of the BRAM protocol will be expected to be very helpful to design and evaluate a MAC (Media Access Control) protocol in wireless LAN systems.