Diffusion magnetic resonance imaging (dMRI) has been widely employed to model the trajectory of myelinated fiber bundles in white matter. Increasingly, dMRI is also used to assess local tissue properties throughout the brain. In the cerebral cortex, myelin content is a critical indicator of the maturation, regional variation, and disease related degeneration of gray matter tissue. Gray matter myelination can be measured and mapped using several non-diffusion MRI strategies; however, first order diffusion statistics such as fractional anisotropy (FA) show only weak spatial correlation with cortical myelin content. Here we show that a simple higher order diffusion parameter, the mean diffusion kurtosis (MK), is strongly correlated with the laminar and regional variation of myelin in the primate cerebral cortex. We carried out ultra-high resolution, multi-shelled dMRI in ex vivo marmoset monkey brains and compared dMRI parameters from a number of higher order models (diffusion kurtosis, NODDI and MAP MRI) to the distribution of myelin obtained using histological staining, and via Magnetization Transfer Ratio MRI (MTR), a non-diffusion MRI method. In contrast to FA, MK closely matched the myelin content assessed by histology and by MTR in the same sample. The parameter maps from MAP-MRI and NODDI also showed good correspondence with cortical myelin content. The results demonstrate that dMRI can be used to assess the variation of local myelin content in the primate cortical cortex, which may be of great value for assessing tissue integrity and tracking disease in living human patients.