The recent explosive growth in the Internet technology has made it imperative to have a network which provides a very high bandwidth. Optical networks employing wavelength division multiplexing (WDM) technology are becoming a viable solution to meet this ever-increasing bandwidth demand. Optical burst switching (OBS) networks provide a good solution for a very high traffic influx which is generally bursty in nature. In this, a single control packet is sent for a group of packets which constitute a data burst with a time gap between them to ensure pure optical switching of bursts. Usually bursts that traverse longer paths are more likely to be dropped than those that traverse shorter paths resulting in fairness problem. Fairness means that for all ingress-egress node pairs in a network a burst must have equal likelihood to get through independent of the hop length involved. In this paper, we develop an efficient fairness method to achieve fairness among bursts with different hop counts. The key idea is to collect scheduling statistics by observing the bursts, and based on this information assign different offset time to bursts with different hop counts. Apart from ensuring fairness our method has several attractive features. By using the online statistics, our methods inherently captures the traffic loading patterns and network topological connectivity. It also ensures that the delay experienced by a burst is low and shorter-hop bursts are not over-penalized while improving the performance of longer-hop bursts. We demonstrate the effectiveness of our fairness method through extensive simulation experiments for a number of random networks which differ in the number of nodes and topological connectivity.