Recent findings indicate robust associations between socioeconomic status (SES) and brain structure in children, raising questions about the ways in which SES may modify structural brain development. In general, cortical thickness and surface area develop in nonlinear patterns across childhood and adolescence, with developmental patterns varying to some degree by cortical region. Here, we examined whether age-related nonlinear changes in cortical thickness and surface area varied by SES, as indexed by family income and parental education. We hypothesized that SES disparities in age-related change may be particularly evident for language- and literacy-supporting cortical regions. Participants were 1148 typically-developing individuals between 3 and 20 years of age. Results indicated that SES factors moderate patterns of age-associated change in cortical thickness but not surface area. Specifically, at lower levels of SES, associations between age and cortical thickness were curvilinear, with relatively steep age-related decreases in cortical thickness earlier in childhood, and subsequent leveling off during adolescence. In contrast, at high levels of SES, associations between age and cortical thickness were linear, with consistent reductions across the age range studied. Notably, this interaction was prominent in the left fusiform gyrus, a region that is critical for reading development. In a similar pattern, SES factors significantly moderated linear age-related change in left superior temporal gyrus, such that higher SES was linked with steeper age-related decreases in cortical thickness in this region. These findings suggest that SES may moderate patterns of age-related cortical thinning, especially in language- and literacy-supporting cortical regions.