Recent longitudinal neuroimaging and neurophysiological studies have shown that tracking relative age-related changes in neural signals, rather than a static snapshot of a neural measure, could offer higher sensitivity for discriminating typically developing (TD) individuals from those with autism spectrum disorder (ASD). It is not clear, however, which aspects of age-related changes (trajectories) would be optimal for identifying atypical brain development in ASD. Using a large cross-sectional data set (Autism Brain Imaging Data Exchange [ABIDE] repository; releases I and II), we aimed to explore age-related changes in cortical thickness (CT) in TD and ASD populations (age range 6-30 years old). Cortical thickness was estimated from T1-weighted MRI images at three scales of spatial coarseness (three parcellations with different numbers of regions of interest). For each parcellation, three polynomial models of age-related changes in CT were tested. Specifically, to characterize alterations in CT trajectories, we compared the linear slope, curvature, and aberrancy of CT trajectories across experimental groups, which was estimated using linear, quadratic, and cubic polynomial models, respectively. Also, we explored associations between age-related changes with ASD symptomatology quantified as the Autism Diagnostic Observation Schedule (ADOS) scores. While no overall group differences in cortical thickness were observed across the entire age range, ASD and TD populations were different in terms of age-related changes, which were located primarily in frontal and tempo-parietal areas. These atypical age-related changes were also associated with ADOS scores in the ASD group and used to predict ASD from TD development. These results indicate that the curvature is the most reliable feature for localizing brain areas developmentally atypical in ASD with a more pronounced effect with symptomatology and is the most sensitive in predicting ASD development.