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Cognitive control and incentive sensitivity are related to overeating and obesity. Optimal white matter integrity is relevant for an efficient interaction among reward-related brain regions. However, its relationship with sensitivity to incentives remains controversial. The aim of this study was to assess the incentive sensitivity and its relationship to white matter integrity in normal-weight and overweight groups. Seventy-six young adults participated in this study: 31 were normal-weight (body mass index [BMI] 18.5 to < 25.0 kg/m2, 14 females) and 45 were overweight (BMI ≥ 25.0 kg/m2, 22 females). Incentive sensitivity was assessed using an antisaccade task that evaluates the effect of incentives (neutral, reward, and loss avoidance) on cognitive control performance. Diffusion tensor imaging studies were performed to assess white matter integrity. The relationship between white matter microstructure and incentive sensitivity was investigated through tract-based spatial statistics. Behavioral antisaccade results showed that normal-weight participants presented higher accuracy (78.0 vs. 66.7%, p = 0.01) for loss avoidance incentive compared to overweight participants. Diffusion tensor imaging analysis revealed a positive relationship between fractional anisotropy and loss avoidance accuracy in the normal-weight group (p < 0.05). No relationship reached significance in the overweight group. These results support the hypothesis that white matter integrity is relevant for performance in an incentivized antisaccade task.