Studying the emergence of distinctive human growth patterns is essential to understanding the evolution of our species. The large number of Neandertal fossils makes this species the best candidate for a comparative study of growth patterns in archaic and modern humans. Here, Neandertal height growth during infancy and early childhood is described using a mathematical model. Height growth velocities for individuals five years old or younger are modelled as age functions based on different estimates of height and age for a set of ten Neandertal infants and children. The estimated heights of each Neandertal individual are compared with those of two modern human populations based on longitudinal and cross-sectional data. The model highlights differences in growth velocity during infancy (from the age of five months onward). We find that statural growth in Neandertal infants is much slower than that seen in modern humans, Neandertal growth is similar to modern humans at birth, but decreases around the third or fourth month. The markedly slower growth rates of Neandertal infants may be attributable to ontogenetic constraints or to metabolic stress, and contribute to short achieved adult stature relative to modern humans.