Motoric cognitive risk (MCR) syndrome is a type of pre-dementia. It is defined as the co-occurrence of subjective cognitive complaints and a slow gait speed. A recent study found that handgrip strength (HGS) asymmetry is associated with an increased risk of neurodegenerative disorders. We aimed to investigate the associations of HGS weakness and asymmetry separately and together with MCR incidence among older Chinese adults. Data from the 2011 and 2015 waves of the China Health and Retirement Longitudinal Study were used. HGS values <28 kg for male participants and <18 kg for female participants were considered HGS weaknesses. HGS asymmetry was assessed by the ratio of nondominant to dominant HGS. We used 3 different cutoff values of HGS ratio to define asymmetry, including 10%, 20%, and 30%. Specifically, HGS ratios <0.90 or >1.10 (10%), <0.80 or >1.20 (20%), and <0.70 or >1.30 (30%) were classified as asymmetry. The participants were classified into 4 groups: neither weakness nor asymmetry (neither), asymmetry only, weakness only, and weakness and asymmetry (both). The association between baseline HGS status and 4-year incidence of MCR was examined using logistic regression analyses. A total of 3,777 participants 60 years and older were included in the baseline analysis. The prevalence of MCR at the baseline was 12.8%. Participants with asymmetry only, weakness only, and both showed significantly increased risk of MCR. After excluding participants with MCR at baseline, 2,328 participants were included in the longitudinal analysis. There were 111 MCR cases (4.77%) over the 4-year follow-up period. Participants with HGS weakness and asymmetry together at baseline had increased odds of incident MCR (HGS ratio at 10%: odds ratio [OR] 4.48, p < 0.001; HGS ratio at 20%: OR 5.43, p < 0.001; HGS ratio at 30%: OR 6.02, p < 0.001). These results show that the presence of both HGS asymmetry and weakness is associated with MCR incidence. The early recognition of HGS asymmetry and weakness may be helpful in the prevention and treatment of cognitive dysfunction.