Multiple neurological complications have been associated with the coronavirus disease-19 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2. This is a narrative review to gather information on all aspects of COVID-19 in elderly patients with cognitive impairment. First, the following three mechanisms have been proposed to underlie the neurological complications associated with COVID-19: 1) direct invasion, 2) immune and inflammatory reaction, and 3) hypoxic brain damage by COVID-19. Next, because the elderly dementia patient population is particularly vulnerable to COVID-19, we discussed risk factors and difficulties associated with cognitive disorders in this vulnerable population. We also reviewed the effects of the patient living environment in COVID-19 cases that required intensive care unit (ICU) care. Furthermore, we analyzed the impact of stringent social restrictions and COVID-19 pandemic-mediated policies on dementia patients and care providers. Finally, we provided the following strategies for working with elderly dementia patients: general preventive methods; dementia care at home and nursing facilities according to the activities of daily living and dementia characteristics; ICU care after COVID-19 infection; and public health care system and government response. We propose that longitudinal follow-up studies are needed to fully examine COVID-19 associated neurological complications, such as dementia, and the efficacy of telemedicine/telehealth care programs.