Processing speed is an important contributor to working memory performance and fluid intelligence in young children. Myelinated white matter plays a central role in brain messaging, and likely mediates processing speed, but little is known about the relationship between myelination and processing speed in young children. In the present study, processing speed was measured through inspection times, and myelin volume fraction (VFM) was quantified using a multicomponent magnetic resonance imaging (MRI) approach in 2- to 5-years of age. Both inspection times and VFM were found to increase with age. Greater VFM in the right and left occipital lobes, the body of the corpus callosum, and the right cerebellum was significantly associated with shorter inspection times, after controlling for age. A hierarchical regression showed that VFM in the left occipital lobe predicted inspection times over and beyond the effects of age and the VFM in the other brain regions. These findings are consistent with the hypothesis that myelin supports processing speed in early childhood.