In this study whether the expectancy belief has a mediating role in the correlation between cost value perception and task value perception of gifted students towards mathematics was examined. It is predicted that the correlation between cost value and task value perceptions of gifted students towards mathematics can change according to their expectancy belief levels. This may shed light on the studies aiming to identify the factors affecting gifted students' motivational beliefs towards mathematics and aiming to improve their mathematics performance. This study is conducted through relational screening model. Relational screening models aim to define the presence and degree of change between two or more variables. In this study, the presence and degree of correlation between expectancy belief, task value and task difficulty perceptions of gifted students towards mathematics are examined. 203 fifth and sixth-grade gifted students who were studying at the Art and Science Centers in 12 different cities in Turkey participated in the study. To identify the expectancy belief, task value and cost value perceptions of gifted students participating in the study towards mathematics were measured by Self and Task Perception Questionnaire. According to the results, when expectancy belief is included in the model as a mediating variable, the direct effect of cost on task value decreases and becomes statistically insignificant. In the mediation model, a major part of the direct effect of cost value perception on task value perception occurs through expectancy belief indirectly. It is understood that expectancy belief has a full mediating role in the correlation between cost value and task value perceptions. Expectancy belief of gifted students towards mathematics has a mediating role in the correlation between cost value and task value perceptions. Thus, the expectancy belief perception towards mathematics is of great importance for gifted students and it has a determining role in the correlation between cost value and task value perceptions.