The human brain develops rapidly during 32–45 postmenstrual weeks (PMW), a critical stage characterized by dramatic increases of metabolic demand. The increasing metabolic demand can be inferred through measurements of regional cerebral blood flow (CBF), which might be coupled to regional metabolism in preterm brains. Arterial spin labeled (ASL) perfusion MRI is one of the few viable approaches for imaging regional CBF of preterm brains, but must be optimized for the extremely slow blood velocity unique in preterm brains. In this study, we explored the spatiotemporal CBF distribution in newborns scanned at the age of 32–45PMW using a pseudo-continuous ASL (pCASL) protocol adapted to slow blood flow in neonates. A total of 89 neonates were recruited. PCASL MRI was acquired from 34 normal newborns and phase contrast (PC) images from 19 newborns. Diffusion tensor images (DTI) were acquired from all 89 neonates for measuring cortical fractional anisotropy (FA), which characterizes cortical microstructure. Reproducible CBF measurements were obtained with the adjusted pCASL sequence. Global CBF measurement based on PC MRI was found to double its value in the 3rd trimester. Regional CBF increases were heterogeneous across the brain with a significantly higher rate of CBF increase in the frontal lobe and a lower rate of CBF increase in the occipital lobe. A significant correlation was found between frontal cortical CBF and cortical FA measurements (p<0.01). Increasing CBF values observed in the frontal lobe corresponded to lower FA values, suggesting that dendritic arborization and synaptic formation might be associated with an elevated local CBF. These results offer a preliminary account of heterogeneous regional CBF increases in a vital early developmental period and may shed the light on underlying metabolic support for cortical microstructural changes during the developmental period of 32–45PMW. Preterm effects and limitations of pCASL techniques in newborns need to be carefully considered for interpretation these results.