In current air traffic control system and especially in free flight method, the resolution of conflicts between different aircrafts is a critical problem. In recent years, conflict detection and resolution problem has been an active and hot research topic in the aviation industry. In this paper, we mapped the aircrafts’ conflict resolution process to graph coloring problem, then we used a prioritization method to solve this problem. Valid and optimal solutions for corresponding graph are equivalent to free conflict flight plans for aircrafts in airspace. The proposed prioritization method is based on some score allocation metrics. After score allocation process, how much the score of an aircraft be higher its priority will be higher and vice versa how much the score of an aircraft be lower its priority will be lower. We implemented and tested our proposed method by different test cases and test results indicate high efficiency of this method.