To investigate the associations between the geriatric nutritional risk index (GNRI) with cognitive functions among U.S. older adults. (Patients were classified into two nutrition risk groups based on the GNRI). Our analysis utilized data from the cross-sectional National Health and Nutrition Examination Survey (NHANES) conducted between 2011 and 2014. Cognitive function was measured using CERAD test, AFT and DSST. Composite z-scores were obtained by summing test-specific z-scores of the above three cognitive tests and were used to assess the global cognitive function. We employed weighted logistic regression models to evaluate the associations between GNRI and nutritional status (low and high GNRI) with cognitive function among older participants. The non-linear relationship was described using fitted smoothed curves and threshold effect analyses. Subgroup analysis and interaction tests were also conducted. This study included 2,592 older participants aged 60 years and older. After adjusting for confounding variables, the GNRI was positively associated with AFT (β = 0.05, 95% CI 0.005-0.096, p-value = 0.0285), DSST (β = 0.192, 95% CI 0.078-0.305, p-value = 0.0010) and the composite z-scores (β = 0.027, 95% CI 0.010-0.044, p-value = 0.0024). The results also showed that the high-GNRI group was significantly associated with AFT (β = 0.922, 95% CI 0.166-1.677, p-value = 0.0169), DSST (β = 2.791, 95% CI 0.884-4.698, p-value = 0.0042) and composite z-scores (β = 0.405, 95% CI 0.115-0.695, p-value = 0.0062) likewise had significant positive correlations, using the low-GNRI group as a reference. In addition, inflection points with CERAD and composite z-scores were found at GNRI of 108.016, and 105.371, respectively. Specifically, on the left side of the inflection point GNRI levels were positively correlated with CERAD and composite z-scores (CERAD β = 0.087, 95% CI 0.024-0.150, p-value = 0.0070; composite z-scores β = 0.065, 95% CI 0.040-0.091, p-value <0.0001), while on the right side of the inflection point were significantly negatively associated (CERAD β = -0.295, 95% CI -0.529 to -0.062, p-value = 0.0133, composite z-scores β = -0.050, 95% CI -0.091 to -0.008, p-value = 0.0184). Lower GNRI was associated with poorer performance in several cognitive domains. Additionally, there was a non-linear positive association between GNRI and cognitive function in normal nutritional states, for excessive GNRI may cause cognitive decline.