Background: The infant brain grows quickly with elaborate microstructural development during the neonatal period. The white matter, during critical periods of development, is selectively vulnerable to altered maturation and impaired growth in very-low-birth-weight (VLBW) infants. Objective: To evaluate whether abnormal white matter maturation in VLBW infants is associated with poor neurodevelopmental outcomes at 18 months of corrected age. Methods: Between 2015 and 2017, we recruited 60 VLBW infants at 24–32 weeks of gestational age and 15 full-term controls. All participants underwent magnetic resonance imaging at near-term age and were assessed at 18 months of corrected age with the Bayley Scales of Infant and Toddler Development, Third Edition. The associations between regional white matter fractional anisotropy (FA) and mean diffusivity on diffusion tensor imaging (DTI) and developmental outcomes were explored using multivariable linear regression after correcting for gestational age, postmenstrual age at DTI scan, and maternal education level. Results: The FA values of the splenium of the corpus callosum (p = 0.032), corticospinal tract (p = 0.025), middle cerebellar peduncle (MCP) (p < 0.001), and cingulum (p = 0.043) were significantly related to cognitive scores; however, only the association corresponding to the MCP remained significant after correcting for multiple comparisons. The MCP FA (p = 0.008) was associated with motor scores after correction for multiple comparisons (p = 0.008). Cognitive impairment (area under the curve [AUC] = 0.823, 95% confidence interval [CI] = 0.722–0.911) and motor impairment (AUC = 0.776, 95% CI = 0.656–0.899) were predicted by MCP FA. Conclusions: The FA of MCP at near-term age may predict developmental outcomes of VLBW infants at 18 months of corrected age.