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A new MAC algorithm is proposed for media access control in decentralized wireless networks. According to geometric distribution, random length bursts are used to repeatedly eliminate channel access nodes, in which each sending node can perform carrier listening operation or a short burst or interference transmission in each time slot. The probability that m nodes out of n nodes survive in the elimination stage of single elimination and repeated eliminations and the probability that one node becomes the only winner in the repeated eliminations are calculated. Based on the basic priority vector, a relative priority mechanism is proposed to realize differentiated services, so as to improve the total channel utilization of the whole network. The simulation experiment results show that the proposed protocol algorithm has obvious advantages in channel access success rate, channel utilization rate and channel allocation fairness compared with several MAC protocols widely used at present.