Premature birth has been associated with poor neurodevelopmental outcomes. However, the relation between such outcomes and brain growth in the neonatal period has not yet been fully elucidated. This study investigates longitudinal brain development between birth and term-equivalent age (TEA) by quantitative imaging in a cohort of premature infants born between 26 and 36 weeks gestational age (GA), to provide insight into the relation of brain growth with later neurodevelopmental outcomes. Longitudinal T2-weighted magnetic resonance images (MRI) of 84 prematurely born infants acquired shortly after birth and TEA were automatically segmented into cortical gray matter (CGM), unmyelinated white matter (UWM), subcortical gray matter (SGM), cerebellum (CB) and cerebrospinal fluid (CSF). General linear models and correlation analysis were used to study the relation between brain volumes and their growth, and perinatal variables. To investigate the ability of the brain volumes to predict children's neurodevelopmental outcome at 18-24 months and at 5 years of age, a linear discriminant analysis classifier was tested and several general linear models were fitted and compared by statistical tests. From birth to TEA, relative volumes of CGM, CB and CSF with respect to total intracranial volume increased, while relative volumes of UWM and SGM decreased. The fastest growing tissues between birth and TEA were found to be the CB and the CGM. Lower GA at birth was associated with lower growth rates of CGM, CB and total tissue. Among perinatal factors, persistent ductus arteriosus was associated with lower SGM, CB and IC growth rates, while sepsis was associated with lower CSF and intracranial volume growth rates. Model comparisons showed that brain tissue volumes at birth and at TEA contributed to the prediction of motor outcomes at 18-24 months, while volumes at TEA and volume growth rates contributed to the prediction of cognitive scores at 5 years of age. The family socio-economic status (SES) was not correlated with brain volumes at birth or at TEA, but was strongly associated with the cognitive outcomes at 18-24 months and 5 years of age. This study provides information about brain growth between birth and TEA in premature children with no focal brain lesions, and investigates their association with subsequent neurodevelopmental outcome. Parental SES was found to be a major determinant of neurodevelopmental outcome, unrelated to brain growth. However, further research is necessary in order to fully explain the variability of neurodevelopmental outcomes in this population.