There is a need for measures that can prevent the onset of dementia in the rapidly aging population. Reportedly, sustained physical exercise can prevent cognitive decline and disability. This study aimed to assess the feasibility of a 12-week physical exercise intervention (PEI) for delay of cognitive decline and disability in the at-risk elderly population in Korea. Twenty-six participants (aged 67.9 ± 3.6 years, 84.6% female) at risk of dementia were assigned to facility-based PEI (n = 15) or home-based PEI (n = 11). The PEI program consisted of muscle strength training, aerobic exercise, balance, and stretching using portable aids. Feasibility was assessed by retention and adherence rates. Physical fitness/cognitive function were compared before and after the PEI. Retention and adherence rates were 86.7% and 88.3%, respectively, for facility-based PEI and 81.8% and 62.3% for home-based PEI. No intervention-related adverse events were reported. Leg strength/endurance and cardiopulmonary endurance were improved in both groups: 30 s sit-to-stand test (facility-based, p = 0.002; home-based, p = 0.002) and 2 -min stationary march (facility-based, p = 0.001; home-based, p = 0.022). Cognitive function was improved only after facility-based PEI (Alzheimer’s Disease Assessment Scale-cognitive total score, p = 0.009; story memory test on Literacy Independent Cognitive Assessment, p = 0.026). We found that, whereas our PEI is feasible, the home-based program needs supplementation to improve adherence.