Cognitive function is crucial during aging. This study assessed the cognitive function of European adults aged 50 and over in relation to handgrip strength and physical inactivity. Study Design: This was a cross-sectional survey. Data were collected from 41,395 adults from 27 European countries participating in the Survey of Health, Ageing, and Retirement in Europe (SHARE) during 2019-2020. Cognitive function was assessed based on five tests, and cognitive impairment was defined using 3+tests. Handgrip strength and physical inactivity were also correlated through the analysis of covariance using a complex study design. The majority of participants were female (56.6%), with a mean age of 70.9 years, and 22.6% presented multimorbidity. Furthermore, 51.1% had a normal cognitive function, while 13.3% had cognitive impairment (The estimated population was 21,944,722). Moreover, cognitive impairment was more prevalent in females than in males (14.4% vs. 12.0%, P<0.001) in patients with no years of education (P<0.001) and origin from southern European countries (P<0.001). Additionally, participants with cognitive impairment had lower mean handgrip strength compared to those with cognitive impairment in 1-2 criteria or with normal cognitive function (29.3 vs. 33.4 and 35.1 kg, respectively, P<0.001). Physically inactive participants had higher odds ratio (OR) of cognitive impairment than those engaging in moderate/vigorous physical activity, both in 1-2 tests (OR:1.73, 95% confidence interval (CI): 1.32-2.26) and in 3+tests (OR: 3.36, 95% CI: 2.57-4.40). Cognitive impairment presented low prevalence and was associated with low levels of handgrip strength and physical inactivity. These specific factors may play a special role in early detection, diagnosis, and treatment or may slow down the progression of cognitive impairment.