Binary exponential backoff algorithm is the de-facto medium access control protocol for wireless local area networks, and it has been employed as the standard contention resolution algorithm in multi-hop wireless ad-hoc networks. However, this algorithm does not function well in multi-hop wireless environments due to its several performance issues and technical limitations. In this paper, we propose a simple, efficient, priority provision, and well performed contention resolution algorithm called enhanced binary exponential backoff (E-BEB) algorithm for impartial channel access in multi-hop wireless ad-hoc networks. We also provide a simple and accurate analytical model to study the system saturation throughput of the proposed scheme. Simulations are conducted to evaluate the performance of E-BEB algorithm. The results show that the E-BEB algorithm can alleviate the fairness problem and support multimedia transmission in multi-hop wireless environments.