This cross-sectional study aimed to evaluate the associations of characteristics of hypertension, including hypertension status, duration, blood pressure (BP), and pulse pressure (PP), with two cognitive functions-episodic memory and executive function, in people aged over 45 years. Using 2013 survey of the China Health and Retirement Longitudinal Study (CHARLS) and weighted multiple linear regression, data from 6,732 participants were utilized. After fully adjusted in full sample, a significantly (P 0.05) negative association was found between treated but uncontrolled hypertension and cognition. In people aged 45-59 years, there was no significant association between hypertension and cognition. However, in people aged >= 60 years, the systolic blood pressure (SBP) and PP showed significantly adverse correlations to cognition. The negative association of untreated, treated but uncontrolled hypertension, and elevated PP with cognition increased with aging. In conclusion, this study shows the correlation between hypertension and cognition was age-dependent with greater correlation in older people; uncontrolled hypertension and PP may be used as predictors of the cognitive decline in people >= 75 years.