Objective: There is growing evidence that in adults, higher levels of handgrip strength (HGS) are linked to better cognitive performance. However, the relationship between HGS and cognitive performance has not been sufficiently investigated in special cohorts, such as individuals with hypertension who have an intrinsically higher risk of cognitive decline. Thus, the purpose of this study was to examine the relationship between HGS and cognitive performance in adults with hypertension using data from the Global Ageing and Adult Health Survey (SAGE). Methods: A total of 4486 Chinese adults with hypertension from the SAGE were included in this study. Absolute handgrip strength (aHGS in kilograms) was measured using a handheld electronic dynamometer, and cognitive performance was assessed in the domains of short-term memory, delayed memory, and language ability. Multiple linear regression models were fitted to examine the association between relative handgrip strength (rHGS; aHGS divided by body mass index) and measures of cognitive performance. Results: Overall, higher levels of rHGS were associated with higher scores in short-term memory (β = 0.20) and language (β = 0.63) compared with the lowest tertiles of rHGS. In male participants, higher HGS was associated with higher scores in short-term memory (β = 0.31), language (β = 0.64), and delayed memory (β = 0.22). There were no associations between rHGS and cognitive performance measures in females. Conclusion: We observed that a higher level of rHGS was associated with better cognitive performance among hypertensive male individuals. Further studies are needed to investigate the neurobiological mechanisms, including sex-specific differences driving the relationship between measures of HGS and cognitive performance in individuals with hypertension.