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Loss of brain tissues and cognitive abilities are natural processes of aging, but longitudinal studies are limited. We explored the longitudinal association between global and regional brain measures with cognitive abilities among individuals with normal cognitive status, mild cognitive impairment, and Alzheimer's Disease, including those with stable or progressive cognitive status, from the Alzheimer's Disease Neuroimaging Initiative. Follow-up was conducted approximately every six months for two to three years to classify participants by their cognitive status (n = 814). Mixed effects models were used to measure the longitudinal association between global and regional brain measures with cognitive abilities assessed by the Alzheimer's Disease Assessment cognition sub-scale after controlling for covariates. While whole brain volume (controlling for head size) affected the rate of cognition changes among those with mild cognitive impairment or Alzheimer's, other volumetric and thickness measures (hippocampus volume, ventricles volume, and entorhinal cortex thickness) had differential effects on cognition, but not on the speed of their changes. Results highlight the potential importance of different brain regions on cognition, but perhaps not on the rate of change and should be further investigated.