Studies have reported associations between cortical thickness (CT) and socioeconomic status (SES), as well as between CT and cognitive outcomes. However, findings have been mixed as to whether CT explains links between SES and cognitive performance. In the current study, we hypothesized that this inconsistency may have arisen from the fact that socioeconomic factors (family income and parental education) may moderate the relation between CT and neurocognitive skills. Results indicated that associations between CT and cognitive performance did vary by SES for both language and executive function (EF) abilities. Across all ages, there was a negative correlation between CT and cognitive skills, with thinner cortices associated with higher language and EF scores. Similarly, across all cognitive skills, children from higher-SES homes outperformed their age-matched peers from lower-SES homes. Moderation analyses indicated that the impact of SES was not constant across CT, with SES more strongly predictive of EF skills among children with thicker cortices and more strongly predictive of language skills among children with thinner cortices. This suggests that socioeconomic advantage may in some cases buffer against a neurobiological risk factor for poor performance. These findings suggest that links between brain structure and cognitive processes vary by family socioeconomic circumstance.