This study examines the impact of a resistance-band functional exercise program, compared with a recreational exercise program, on physical fitness and reaction times in persons older than 60 years. Fifty-four community-dwelling volunteers (71.76 ± 6.02 years) were assigned to a specific exercise program: Functional activity program (focused on resistance-band multi-joint activities; experimental group, EG), or recreational physical activity program (with gross motor activities of ludic content; control group, CG). Before and after the intervention, we determined cognitive capacity in terms of simple reaction time (S-RT), choice reaction time (C-RT) and fitness. In both groups physical performance improved, though this improvement was more marked in the EG for grip strength, arm strength and gross motor abilities (p < 0.05). Reaction times were better only in EG (S-RT = 10.70%, C-RT = 14.34%; p < 0.05) after the corresponding physical training intervention. The training period showed no effect on the moderate relationship between both RT and gross motor abilities in the CG, whereas the EG displayed an enhanced relationship between S-RT and grip-strength as well as the C-RT with arm strength and aerobic capacity (r ~ 0.457; p < 0.05). Our findings indicate that a functional exercise program using a resistance band improves fitness and cognitive performance in healthy older adults.