Abstract Low handgrip strength, a hallmark measure of whole-body strength, has been linked with greater odds of cognitive decline and dementia; however, conflicting findings, which could be due to population characteristics and choice of tools, such for the assessment of handgrip strength and cognitive function domains, also exist. Therefore, we examined the relationship of handgrip strength with a comprehensive list of tests to assess domains of cognitive function using a representative sample of US older men and women without neurodegenerative disorders such as dementia. We analyzed cross-sectional data from the US National Health and Nutrition Examination Survey (NHANES) between 2011 and 2014, with a study cohort of 777 older adults (380 men and 397 women) above 60 years of age. Handgrip strength was assessed using a handgrip dynamometer, while cognitive function was assessed through the Consortium to Establish a Registry for Alzheimer’s Disease (CERAD) Word List Learning Test (WLLT), Word List Recall Test (WLRT), Intrusion Word Count Test (WLLT-IC and WLRT-IC), the Animal Fluency Test (AFT), and the Digit Symbol Substitution Test (DSST). Sex-stratified multiple linear regression analyses were performed upon covariate adjustment for age, ethnicity, socio-economic status, education, medical history, body mass index, physical activity, energy, protein, and alcohol intake. Maximal handgrip strength was positively associated with cognitive function scores, including CERAD WLLT (P = 0.009, R² = 0.146) and AFT (P = 0.022, R² = 0.024) in older men, but not in women (CERAD WLLT: P = 0.253, AFT: P = 0.370). No significant associations with CERAD WLLRT (men: P = 0.057, women: P = 0.976), WLLT-IC (men: P = 0.671, women: P = 0.869), WLLRT-IC (men: P = 0.111, women: P = 0.861), and DSST (men: P = 0.108, women: P = 0.091) were observed. Dose–response curves exhibited a prominent linear relationship between all significant associations after covariate adjustment, with no indication of a plateau in these relationships. In conclusion, higher handgrip strength was independently associated with better learning ability for novel verbal information and verbal fluency in US men over the age of 60 and without dementia. Longitudinal studies are required to confirm whether muscle strength independently predicts cognitive function changes in older adults in a sex-specific manner, and whether this connection is affirmed to the possibility of reverse causation due to declines in physical activity levels in the preclinical phase of dementia.