Adolescence is a period of significant brain changes; however, the effects of age and sex on cortical development are yet to be fully characterized. Here, we utilized innovative intrinsic curvature (IC) analysis, along with the traditional cortical measures [cortical thickness (CT), local gyrification index (LGI), and surface area (SA)], to investigate how these indices (1) relate to each other and (2) depend on age and sex in adolescent cortical development. T1-weighted magnetic resonance images from 218 healthy volunteers (age range 8.3–29.2 years, M[SD] = 16.5[3.4]) were collected at two sites and processed with FreeSurfer and Caret software packages. Surface indices were extracted per cortex area (frontal, parietal, occipital, temporal, insula, and cingulate). Correlation analyses between the surface indices were conducted and age curves were modelled using generalized additive mixed-effect models. IC showed region-specific associations with LGI, SA, and CT, as did CT with LGI. SA was positively associated with LGI in all regions and CT in none. CT and LGI, but not SA, were inversely associated with age in all regions. IC was inversely associated with age in all but the occipital region. For all regions, males had larger cortical SA than females. Males also had larger LGI in all regions and larger IC of the frontal area; however, these effects were accounted for by sex differences in SA. There were no age-by-sex interactions. The study of IC adds a semi-independent, sensitive measure of cortical morphology that relates to the underlying cytoarchitecture and may aid understanding of normal brain development and deviations from it.