The purposes of the study are to understand the “drawing a diagram” strategies of mathematically gifted elementary students in solving problems, as well as what kind of different process responded to their questions. This study focused on the exam of students who were elected from the Pre-semifinal of Taiwan Olympiad Math competition in 2003. They were trained to compete in the Asia Pacific Olympiad for Primary Schools. Four students chosen from the contestants were interviewed in the semi-structure way. The research results show that there were four differences from their problem-solving process: (1) the different contents of the diagrammatic representation, (2) the different forms of the diagrammatic representation strategy, (3) the different applications of the diagrammatic representation, and (4) the different evaluations of the answer for the problems.