Dementia is one of the priority public health problems in the older population, and the number of people with dementia is steadily increasing. The longitudinal association of muscle strength with risk of new-onset cognitive dysfunction in a general population including middle and older adults remains unknown. The purpose of this study was to investigate the effects of low muscle strength on risk for new-onset cognitive dysfunction over 6 years using a large nationwide sample of cognitively healthy adults. Study participants included 6,435 middle and older adults (33,554 person-years of follow-up), using data from the Korean Longitudinal Study of Ageing 2006-2012. Muscular strength was measured using the maximum handgrip strength of each participant as an index of muscle quality. Low muscle strength was defined as one standard deviation below the mean using the handgrip strength index based on the study population. Cognitive function was evaluated using the Mini-Mental Status Evaluation. The hazard ratio (HR) for cognitive dysfunction significantly and linearly increased according to muscle strength status independent of potential confounding factors (HR: 1.36, 95% confidence interval CI: 1.18-1.56 for low vs. normal-high group). Using stratified analyses, a significant association between muscle strength status and risk of cognitive impairment was observed in those with low physical activity, but not those with high physical activity. We show that handgrip strength is associated with increased risk of new-onset cognitive dysfunction over 6 years of follow-up in cognitively healthy middle aged and older adults at baseline.