Leptin, a hormone produced by body fat tissue, acts on hypothalamic receptors in the brain to regulate appetite and energy expenditure, and on neurons in the arcuate nucleus to signal that an individual has had enough to eat. Leptin enters the central nervous system at levels that depend on an individual's body fat. Obese people, on average, show greater brain atrophy in old age, so it is valuable to know whether brain atrophy relates to leptin levels, which can be targeted by interventions. We therefore determined how plasma leptin levels, and BMI, relate to brain structure, and whether leptin levels might account for BMI's effect on the brain. We measured regional brain volumes using tensor-based morphometry, in MRI scans of 517 elderly individuals with plasma leptin measured (mean: 13.3±0.6 ng/ml; mean age: 75.2±7.3 years; 321 men/196 women). We related plasma leptin levels to brain volumes at every location in the brain after adjusting for age, sex, and diagnosis and, later, also BMI. Plasma leptin levels were significantly higher (a) in women than men, and (b) in obese versus overweight, normal or underweight individuals. People with higher leptin levels showed deficits in frontal, parietal, temporal and occipital lobes, brainstem, and the cerebellum, irrespective of age, sex, or diagnosis. These associations persisted after controlling for BMI. Greater brain atrophy may occur in people with central leptin insufficiency, a marker of obesity. Therapeutic manipulation of leptin may be a promising direction for slowing brain decline.