What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating creative production ability. Another objective is to develop the self-directed learning attitude of the gifted. To examine the objectives, Mathematical Modeling was applied to the gifted. We analyzed the behaviors of the mathematically gifted students attending the class, which applied Mathematical Modeling to assess the potential for cultivating creative production ability. And in the aspect of the self-directed learning attitudes, two groups were compared: the gifted students who participated in the Mathematical Modeling class and other gifted students who did not. From these results, Mathematical Modeling is proposed as an appropriate program to achieve educational objectives for the mathematically gifted students. (Contains 1 table and 5 figures.)