Background: There have been many studies on the associations between body mass index (BMI) and cognitive function. However, no study has ever compared the associations across the methods of categorizing BMI. In this study, we aimed to fill the gap in the previous studies and examine whether the obesity paradox is valid in the risk of cognitive function. Methods: Of the 10,254 people aged 45 and older from the Korean Longitudinal Study of Ageing from 2006 to 2016, 8,970 people were finalized as the study population. The dependent variable was whether a person has a normal cognitive function or not, and the independent variables of interest were BMI categorized by the World Health Organization Western Pacific Regional Office (WHO-WPRO) method, the WHO method, and a 10-group method. Covariates included sociodemographic factors, health behavior factors, and health status factors. A generalized linear mixed model analysis with a logit link was used. Results: In the adjusted model with all covariates, first, in the case of BMI categories of the WHO-WPRO method, underweight (odds ratio [OR], 1.16; 95% confidence interval [CI], 1.15-1.17), overweight (OR, 1.36; 95% CI, 1.35-1.36), and obese (OR, 1.34; 95% CI, 1.33-1.34) groups were more likely to have a normal cognitive function than a normal-weight group. Next, in the case of BMI categories of the WHO method, compared to a normal-weight group, underweight (OR, 1.15; 95% CI, 1.14-1.16) and overweight (OR, 1.06; 95% CI, 1.06-1.07) groups were more likely to have a normal cognitive function; however, obese (OR, 0.62; 95% CI, 0.61-0.63) group was less likely to have it. Lastly, in the case of the 10-group method, as BMI increased, the likelihood to have a normal cognitive function changed like a wave, reaching a global top at group-7 (26.5 kg/㎡ ≤ BMI <28.0 kg/㎡). Conclusion: The associations between BMI and cognitive function differed according to how BMI was categorized among people aged 45 and older in Korea, which suggests that cognitive function may be positively associated with BMI in some categories of BMI but negatively in its other categories. Health policies to reduce cognitive impairment need to consider this association between BMI and cognitive function.