The purpose of this study was to investigate the relationships between thinking styles and the components of mathematical ability of elementary math gifted children. The results of this study were as follows: First, there were differences in thinking styles: The gifted students prefer legislative, judical, hierarchic, global, internal and liberal thinking styles. General students prefer oligarchic and conservative thinking styles. Second, there were differences in components of mathematical ability: The gifted students scored high in all sections. And if when they scored high in one section, then they most likely scored high in the other sections as well. But the spacial related lowly to the generalization and memorization. There is no significant relationship between memorization and calculation Third, there was a correlation between thinking styles and components of mathematical ability: Some thinking styles were related to components of mathematical ability. In functions of thinking styles, legislative style have higher effect on calculation. And executive, judical styles related negatively to the inference ability. In forms of thinking styles monarchic style had higher effect on space ability, hierarchic style had higher effect on calculation. Monarchic, hierarchic styles related negatively to inference ability. In level of thinking styles global, local styles have higher effect on calculation. Local styles related negatively to the inference ability. In the scope of thinking styles, internal style had a higher effect on generalization, and external style had a higher effect on calculation. And there is no significant relationship leaning of thinking styles.