The burden of cognitive impairment and dementia is particularly severe in low- and middle-income countries. Although hypertension is an important risk factor for cognitive impairment, the influence of different hypertension classification on cognitive impairment remains controversial. To explore the impact of hypertension and hypertension classification on cognitive function, this study was based on a low-income population aged over 60 years in northern China. This population-based, cross-sectional study was conducted from April 2014 to January 2015 in rural areas of Tianjin, China. A total of 1,171 participants aged ≥ 60 years were included. Participants were interviewed by professional researchers face-to-face, using the pre-designed questionnaire. Cognitive function was assessed using the Mini-mental State Examination (MMSE). Multivariate regression analysis was used to calculate the odds ratio (OR) value. There was a significant association between hypertension and cognitive impairment (OR, 1.415; 95% CI: 1.005–1.992; P = 0.047) and a significant positive association between stage 3 hypertension (OR, 1.734; 95% CI: 1.131–2.656; P = 0.012) and the prevalence of cognitive impairment. To prevent dementia, clinicians should consider the cognitive function and blood pressure control of low-income individuals aged over 60 years with hypertension in northern China, especially those with stage 3 hypertension. In addition, the inconsistent effects of blood pressure on different cognitive functions should also be considered; special attention should be paid to orientation and concentration.