Dietary fatty acid intake is closely related to the cognitive function of the overweight and obese population. However, few studies have specified the correlation between exact fatty acids and cognitive functions in different body mass index (BMI) groups. We aimed to explain these relationships and reference guiding principles for the fatty acid intake of the overweight and obese population. Normal weight, overweight, and obese participants were recruited to receive a cognitive function assessment and dietary survey, dietary fatty acids intake was calculated, and the erythrocyte membrane fatty acid profile was tested by performing a gas chromatography analysis. The percentages of saturated fatty acids (SFAs) in the obese group were higher, while monounsaturated fatty acids (MUFAs) and polyunsaturated fatty acids (PUFAs) were lower than in the normal weight and overweight groups. In the erythrocyte membrane, the increase of n-3 PUFAs was accompanied by cognitive decline in the overweight group, which could be a protective factor for cognitive function in the obese group. High n-6 PUFAs intake could exacerbate the cognitive decline in the obese population. Dietary fatty acid intake had different effects on the cognitive function of overweight and obese people, especially the protective effect of n-3 PUFAs; more precise dietary advice is needed to prevent cognitive impairment.