Frailty has been established as a risk factor for falls, and prefrailty also seems a risk; however, few studies have focused on the association between falls and each of the five components of frailty proposed by Fried. In the present study, we sought to elucidate the association between prefrailty and falls, and moreover, the association of frailty component with falls. Participants were community-dwelling older people who had cognitive complaints but not dementia (N = 447, male 54.6%). Prefrailty was defined as exhibiting one or two of the five Fried criteria. Frail individuals were excluded. Background characteristics were compared between the prefrail and robust groups, and multiple regression analysis was performed to investigate the associations between fall history within the past year and factors that were significantly different between the groups. We also performed logistic regression analysis with adjustment for age, education and gender to assess associations with frailty components. We found that prefrailty was associated with fall history. Depressed mood was also significantly associated with fall history. Among the five frailty criteria, exhaustion was significantly associated with falls. Prefrailty, especially the criteria of exhaustion, and depressed mood were associated with fall history.