The apolipoprotein E ɛ4 allele is the primary genetic risk factor for the sporadic type of Alzheimer's disease. However, the mechanisms by which apolipoprotein E ɛ4 are associated with neurodegeneration are still poorly understood. We applied the Neurite Orientation Dispersion Model to characterize the effects of apolipoprotein ɛ4 and its interactions with age and education on cortical microstructure in cognitively normal individuals. Data from 1954 participants were included from the PREVENT-Dementia and ALFA (ALzheimer and FAmilies) studies (mean age = 57, 1197 non-carriers and 757 apolipoprotein E ɛ4 carriers). Structural MRI datasets were processed with FreeSurfer v7.2. The Microstructure Diffusion Toolbox was used to derive Orientation Dispersion Index maps from diffusion MRI datasets. Primary analyses were focused on (i) the main effects of apolipoprotein E ɛ4, and (ii) the interactions of apolipoprotein E ɛ4 with age and education on lobar and vertex-wise Orientation Dispersion Index and implemented using Permutation Analysis of Linear Models. There were apolipoprotein E ɛ4 × age interactions in the temporo-parietal and frontal lobes, indicating steeper age-dependent Orientation Dispersion Index changes in apolipoprotein E ɛ4 carriers. Steeper age-related Orientation Dispersion Index declines were observed among apolipoprotein E ɛ4 carriers with lower years of education. We demonstrated that apolipoprotein E ɛ4 worsened age-related Orientation Dispersion Index decreases in brain regions typically associated with atrophy patterns of Alzheimer's disease. This finding also suggests that apolipoprotein E ɛ4 may hasten the onset age of dementia by accelerating age-dependent reductions in cortical Orientation Dispersion Index.