In this paper, a new adaptive minimum contention window binary exponential backoff algorithm (referred to as AWBEB algorithm) is proposed to improve the performance of IEEE 802.11 Distributed Coordination Function (DCF) scheme, which is widely used for Ad Hoc networks and wireless LAN. We model the AWBEB algorithm scheme via establishing a bidimensional discrete-time Markov Chain, and the stationary distribution probabilities of AWBEB algorithm are derived. The performance of AWBEB algorithm is analyzed, and then AWBEB algorithm is simulated by computer programming. The analytical and numerical results show that the system saturation throughput and medium access delay of a packet for a given number of nodes N are better than the DCF algorithm.