Dramatic changes of the human brain during the first year of postnatal development are poorly understood due to their multifold complexity. In this paper,we present the first attempt to jointly predict,using neonatal data,the dynamic growth pattern of brain cortical surfaces (collection of 3D triangular faces) and fiber tracts (collection of 3D lines). These two entities are modeled jointly as a multishape (a set of interlinked shapes). We propose a hybrid learning-based multishape prediction framework that captures both the diffeomorphic evolution of the cortical surfaces and the non-diffeomorphic growth of fiber tracts. In particular,we learn a set of geometric and dynamic cortical features and fiber connectivity features that characterize the relationships between cortical surfaces and fibers at different timepoints (0,3,6,and 9 months of age). Given a new neonatal multishape at 0 month of age,we hierarchically predict,at 3,6 and 9 months,the postnatal cortical surfaces vertex-by-vertex along with fibers connected to adjacent faces to these vertices. This is achieved using a new fiber-to-face metric that quantifies the similarity between multishapes. For validation,we propose several evaluation metrics to thoroughly assess the performance of our framework. The results confirm that our framework yields good prediction accuracy of complex neonatal multishape development within a few seconds.