In conventional neonatal MRI, the T2 hyperintensity (T2h) in cerebral white matter (WM) at term-equivalent age due to immaturity or impairment is still difficult to identify. To clarify such issue, this study used the metrics derived from a two-compartment WM model of diffusional kurtosis imaging (WM-DKI), including intra-axonal, extra-axonal axial and radial diffusivities (Da, De,// and De,⊥), to compare WM differences between the simple T2h and normal control for both preterm and full-term neonates, and between simple T2h and complex T2h with hypoxic-ischemic encephalopathy (HIE). Results indicated that compared with control, the simple T2h showed significantly increased De,// and De,⊥, but no significant change in Da in multiple premyelination regions, indicative of expanding extra-axonal diffusion microenvironment; while myelinated regions showed no changes. However, compared with simple T2h, the complex T2h with HIE had decreased Da, increased De,⊥ in both premyelination and myelinated regions, indicative of both intra- and extra-axonal diffusion alterations. While diffusion tensor imaging (DTI) failed to distinguish simple T2h from complex T2h with HIE. In conclusion, superior to DTI-metrics, WM-DKI metrics showed more specificity for WM microstructural changes to distinguish simple T2h from complex T2h with HIE.