Given the limited channel capacity in wireless LANs, it is important to achieve high throughput and good fairness through medium access control (MAC) schemes. Although many schemes have been proposed to enhance throughput or fairness of the original IEEE 802.11 standard, they either fail to consider both throughput and fairness, or to do so with complicated algorithms. In this paper, we propose a new MAC scheme that dynamically optimizes each active node's backoff process. The key idea is to enable each node to adjust its Contention Window (CW) to approach the optimal one that will maximize the throughput. Meanwhile, when the network enters into steady state in saturated case, i.e., under heavy traffic load, all the nodes will maintain approximately identical CWs, which guarantees fair share of the channel among all nodes. A distinguishing feature of this scheme is the use of an index called average channel idle interval for optimizing the backoff process without estimating the number of active nodes in networks. We show through theoretical analysis that the average channel ideal interval can represent current network traffic load and indicate the optimal CW. Moreover, since it can be obtained through direct measurement, our scheme eliminates the need for complicated estimation of the number of active nodes as required in previous schemes, which makes our schemes simpler and more reliable when network traffic changes frequently. Through simulation comparison with previous schemes, we show that our scheme can greatly improve the throughput no matter the network is in saturated or non-saturated case, while maintaining good fairness.