In this paper, we propose a new prioritized Optical Burst Switching (OBS) protocol based on a hop count, which can provide efficient utilization in optical networks. Under several legacy schemes, a switch drops the burst with the shortest time regardless of its traversed hop count. As a result, a dropped burst that have been traversed many hops might cause increased bandwidth waste compared to one that has traversed a few hops. To improve this problem, we propose the Just Enough Time (JET) with a hop counting scheme which can reduce the wasted bandwidth by prioritizing the burst traversed many hops over others. From the simulation result, it is preyed, we show that the proposed scheme has advantages against legacy schemes in terms of the burst blocking probability and the link utilization.