Human brain exhibits structural and functional asymmetries. How the left-lateralization in white matter changes with age from newborns through childhood is not fully investigated. In this work, development of the left-lateralization from birth to 13 years is revealed by using tract-based spatial statistics with dynamic age-specific brain templates. Structural left-lateralization with larger fractional anisotropy in motor-related and language-related white matter is already present in newborns. The involvement of corticospinal tract, superior longitudinal fasciculus and uncinate fasciculus into regions with left-lateralization appears at different age. This may be associated with the development of fine motor and language during the early childhood.