Structural brain change and concomitant cognitive decline are the seemingly unavoidable escorts of aging. Despite accumulating studies detailing the effects of age on the brain and cognition, the relationship between white matter features and cognitive function in aging have only recently received attention and remain incompletely understood. White matter microstructure can be measured with diffusion tensor imaging (DTI), but whether DTI can provide unique information on brain aging that is not explained by white matter volume is not known. In the current study, the relationship between white matter microstructure, age, and neuropsychological function was assessed using DTI in a statistical framework that employed white matter volume as a voxel-wise covariate in a sample of 120 healthy adults across a broad age range (18-83). Memory function and executive function were modestly correlated with the DTI measures while processing speed showed the greatest extent of correlation. The results suggest that age-related white matter alterations underlie age-related declines in cognitive function. Mean diffusivity and fractional anisotropy in several white matter brain regions exhibited a nonlinear relationship with age, while white matter volume showed a primarily linear relationship with age. The complex relationships between cognition, white matter microstructure, and white matter volume still require further investigation.