During the second and third trimesters of human gestation, the brain undergoes rapid neurodevelopment thanks to critical processes such as neuronal migration, radial glial scaffolding, and synaptic sprouting. Unfortunately, gathering high-quality MRI data on the healthy fetal brain is complex, making it challenging to understand this development. To address this issue, we conducted a study using motion-corrected diffusion tensor imaging (DTI) to analyze changes in the cortical gray matter (CP) and sub-cortical white matter (scWM) microstructure in 44 healthy fetuses between 23 and 36 weeks of gestational age. We automatically segmented these two tissues and parcellated them into eight regions based on anatomy, including the frontal, parietal, occipital, and temporal lobes, cingulate, sensory and motor cortices, and the insula. We were able to observe distinct patterns of diffusion MRI signals across these regions. Specifically, we found that in the CP, fractional anisotropy (FA) consistently decreased with age, while mean diffusivity (MD) followed a downward-open parabolic trend. Conversely, in the scWM, FA exhibited an upward-open parabolic trajectory, while MD followed a downward-open parabolic trend. Our study underscores the potential for diffusion as a biomarker for normal and abnormal neurodevelopment before birth, especially since most neurodiagnostic tools are not yet available at this stage.