The present invention relates to a composition for improving cognitive ability, and preventing or treating dementia and a hyperactivity disorder, which includes a Galla rhois extract and fraxin as active ingredients. It was identified that the composition including the Galla rhois extract and fraxin significantly improves cognitive memory in an Alzheimer's disease model induced by Aβ (1-42) administration and an APPswe/PS1dE9 double-expressing Alzheimer's disease model, and inhibits the generation of amyloid plaques, suggesting the usefulness of the combination of the Galla rhois extract and fraxin, as a therapeutic material, against Alzheimer's disease, and showing that the combination of the Galla rhois extract and fraxin is able to be used as a therapeutic agent for ADHD.