In this paper, we propose a new prioritized Optical Burst Switching (OBS) protocol based on a hop count, which can provide an efficient utilization in optical Wireless networks. Under several legacy schemes, a switch drops the burst with a shorter time among ones regardless of its traversed hop count. As a result, the dropped burst that have been traversed more hops might cause to waste bandwidth than the one traversed a few hops. Noting that this problem, we propose the Just Enough Time(JET) with a hop count scheme which can reduce the wasted bandwidth by prioritizing the burst traversed more hops over others. From the simulation result, we show that the proposed scheme is advantageous over the legacy schemes in terms of the burst blocking probability and the link utilization.