The authors assessed the cross-sectional association of physical function measures with cognition in the Kaiser Healthy Aging and Diverse Life Experiences Cohort. Analyses included 1369 participants (24% Asian, 26% Black, 18% Latino, 32% White). Grip strength was measured using a hand-held dynamometer (kilograms) and gait speed was measured over a 4-m walk (seconds/meter). The Spanish and English Neuropsychological Assessment Scales was used to evaluate cognitive domains of executive function, semantic memory, and verbal episodic memory. Physical function measures (per SD) were associated with cognitive test z-scores in linear regression models adjusted for demographic, behavioral, and clinical factors. Racial/ethnic differences were tested using interaction terms and stratification. Stronger grip was associated with better executive function [β=0.10 (95% confidence interval, 0.05-0.15)], semantic memory [β=0.13 (0.09-0.18)] and verbal episodic memory [β=0.07 (0.02-0.13)] with no racial/ethnic differences. Faster gait was associated with better executive function [β=0.29 (0.22-0.36)], semantic memory [β=0.23 (0.16-0.30)], and verbal episodic memory [β=0.20 (0.13-0.27)]; however, the association between gait speed and executive function varied by race/ethnicity with the strongest associations in Asians and Whites. Across race/ethnicity, grip strength and gait speed were associated with cognition with racial/ethnic differences in the association of gait speed and executive function.