This study aimed to evaluate the relationship between pulse pressure (PP) and sarcopenia, frailty, and cognitive function in elderly patients with hypertension. We evaluated 435 elderly patients with a history of hypertension who visited the frail outpatient clinic between July 2015 and October 2021. Data at the 1-, 2-, and 3-year follow-ups were available for 222, 177, and 164 patients, respectively. Sarcopenia, frailty, and cognitive function, including Mini-Mental State Examination (MMSE) scores, were evaluated. The patients' mean age was 79.2 ± 6.3 years (male, 34.9%). PP and mean blood pressure (BP) were 60.1 ± 13.6 mmHg and 94.1 ± 13.0 mmHg, respectively. At baseline, lower PP was associated with probable dementia (MMSE score ≤23 points) (OR = 0.960 per 1 mmHg increase; 95% CI, 0.933-0.989; P = 0.006) in the model adjusted for conventional confounding factors and comorbidities, whereas higher PP was associated with low handgrip strength (OR = 1.018 per 1 mmHg increase; 95% CI, 1.001-1.036; P = 0.041). In multivariate-adjusted logistic regression analysis of patients with preserved handgrip strength at baseline, reductions in PP (OR = 0.844; 95% CI, 0.731-0.974; P = 0.020) and mean BP (OR = 0.861; 95% CI, 0.758-0.979; P = 0.022) were significantly associated with the incidence of low handgrip strength at 3 years. In conclusion, a higher PP induced by increased arterial stiffness was associated with lower handgrip strength, whereas a lower PP was associated with probable dementia. Reduced PP was associated with decreased handgrip strength after three years.