Abstract Genetic influences on cortical thickness (CT) and surface area (SA) are known to vary across the life span. Little is known about the extent to which genetic factors influence CT and SA in infancy and toddlerhood. We performed the first longitudinal assessment of genetic influences on variation in CT and SA in 501 twins who were aged 0–2 years. We observed substantial additive genetic influences on both average CT (0.48 in neonates, 0.37 in 1-year-olds, and 0.44 in 2-year-olds) and total SA (0.59 in neonates, 0.74 in 1-year-olds, and 0.73 in 2-year-olds). In addition, we found strong heritability of the change in average CT (0.49) from neonates to 1-year-olds, but not from 1- to 2–year-olds. Moreover, we found strong genetic correlations for average CT (rG = 0.92) between 1- and 2-year-olds and strong genetic correlations for total SA across all timepoints (rG = 0.96 between neonates and 1-year-olds, rG = 1 between 1- and 2-year-olds). In addition, we found CT and SA are strongly genetic correlated at birth, but weaken over time. Overall, results suggest a dynamic genetic relationship between CT and SA during first 2 years of life and provide novel insights into how genetic influences shape the cortical structure during early brain development.