We present a data-driven method to build a spatiotemporal statistical shape model predictive of normal cranial growth from birth to the age of 2 years. The model was constructed using a normative cross-sectional computed tomography image dataset of 278 subjects. First, we propose a new standard representation of the calvaria using spherical maps to establish anatomical correspondences between subjects at the cranial sutures – the main areas of cranial bone expansion. Then, we model the cranial bone shape as a bilinear function of two factors: inter-subject anatomical variability and temporal growth. We estimate these factors using principal component analysis on the spatial and temporal dimensions, using a novel coarse-to-fine temporal multi-resolution approach to mitigate the lack of longitudinal images of the same patient. Our model achieved an accuracy of 1.54 ± 1.05 mm predicting development in an independent longitudinal dataset. We also used the model to calculate the cranial volume, cephalic index and cranial bone surface changes during the first two years of age, which were in agreement with clinical observations. To the best of our knowledge, this is the first data-driven and personalized predictive model of cranial bone shape development during infancy and it can serve as a baseline to study abnormal growth patterns in the population.