In optical burst switching (OBS) networks, burst with different numbers of hops experience unfairness in terms of the burst loss probability. In this paper, we propose a preemptive scheme based on the number of transit hops in OBS networks. In our proposed scheme, preemption is performed with two thresholds; one is for the total number of hops of a burst and the other is for the number of transit hops the burst has passed through. We evaluate the performance of the scheme by simulation, and numerical examples show that the proposed scheme improves the fairness among the bursts with different numbers of hops, keeping the overall burst loss probability the same as that for the conventional OBS transmission without preemption.