The paper proposes and analyzes an adaptive p-persistent-based (APP) medium access control (MAC) scheme for IEEE 802.11 WLAN. The APP MAC scheme intends to support delay fairness for every station in each access, denoting small delay variance. It differentiates permission probabilities of transmission for stations which are incurred with various packet delays. This permission probability is designed as a function of the numbers of retransmissions and re-backoffs so that stations with larger packet delay are endowed with higher permission probability. Also, the scheme is analyzed by a Markov-chain analysis, where the collision probability, the system throughput, and the average delay are successfully obtained. Numerical results show that the proposed APP MAC scheme can attain lower mean delay and higher mean throughput. In the mean time, simulation results are given to justify the validity of the analysis, and also show that the APP MAC scheme can achieve more delay fairness than conventional algorithms.