White matter in human brain undergoes a complex and long lasting process. It is not likely that conventional diffusion parameters are specific enough to distinguish axon-related and myelin-related processes. This study investigates directional diffusivities in intra-axonal and extra-axonal compartments on preterm neonates, term neonates, infants, and adults. Two change patterns of extra-axonal axial and radial diffusivities are found during development. This may be related to premyelination and myelination. Developmental changes of the fiber dispersion and intra-axonal diffusivities are observed in both pre-myelination and myelination periods. Directional diffusivities in intra-axonal and extra-axonal compartments provide more detailed information to evaluate axonal development.