Healthy neurocognitive aging has been associated with the microstructural degradation of white matter pathways that connect distributed gray matter regions, assessed by diffusion-weighted imaging (DWI). However, the relatively low spatial resolution of standard DWI has limited the examination of age-related differences in the properties of smaller, tightly curved white matter fibers, as well as the relatively more complex microstructure of gray matter. Here, we capitalize on high-resolution multi-shot DWI, which allows spatial resolutions < 1 mm3 to be achieved on clinical 3T MRI scanners. We assessed whether traditional diffusion tensor-based measures of gray matter microstructure and graph theoretical measures of white matter structural connectivity assessed by standard (1.5 mm3 voxels, 3.375 μl volume) and high-resolution (1 mm3 voxels, 1μl volume) DWI were differentially related to age and cognitive performance in 61 healthy adults 18–78 years of age. Cognitive performance was assessed using an extensive battery comprising 12 separate tests of fluid (speed-dependent) cognition. Results indicated that the high-resolution data had larger correlations between age and gray matter mean diffusivity, but smaller correlations between age and structural connectivity. Moreover, parallel mediation models including both standard and high-resolution measures revealed that only the high-resolution measures mediated age-related differences in fluid cognition. These results lay the groundwork for future studies planning to apply high-resolution DWI methodology to further assess the mechanisms of both healthy aging and cognitive impairment.