This paper deals with assigning defensive counter air aircraft to the moving target in the air. Recently various kinds of allocation problems have been researched for fixed targets using offensive aircrafts. However, the counter air allocation problems for attacking aircrafts with considering the time and the threat have not been studied much. The main objective of this study is to mininize the time to intercept and the threat values simultaneously by using goal programming. The optimal solution by using an integer goal programming and a branch and bound algorithm is found and analyzed. By applying this model to real situation, we expect to reduce the time and number of sorties for destroying enemy aircraft, respectively.