A model is proposed to analyze the MAC (medium access control) access delay of EDCA (enhanced distribution channel access) mechanism of wireless LANs (local area networks), which is based on the moment generating function and signal flow graph. The model gives the probability distribution function (PDF) of MAC access delay and several relative characteristic numbers, including the mean value, variance, standard deviation and deviation coefficient of MAC access delay. The results of the analytical model coincide with simulations, which validates the model proposed. A lot of analyses are presented. Firstly, the model presents the relationship among number of nodes and sending probability, collision probability, freezing probability and mean delay of all ACs (access categories). Secondly, the model discloses the composition of MAC access delay. Thirdly, the model presents the effect of different values of AIFS (arbitration inter frame spacing) on MAC access delay. Lastly, the model presents that the deviation coefficient of MAC access delay is larger than 1, so when the exponential distribution is adopted as the distribution of MAC access delay, the capacity of the queue system will be evaluated wrongly.