The prevailing coronavirus disease-19 (COVID-19) caused by a novel severe acute respiratory syndrome coronavirus (SARS-CoV-2) has presented some neurological manifestations including hyposmia, hypogeusia, headache, stroke, encephalitis, Guillain–Barre syndrome, and some neuropsychiatric disorders. Although several cell types in the brain express angiotensin-converting enzyme-2 (ACE2), the main SARS-CoV-2 receptor, and other related proteins, it remains unclear whether the observed neurological manifestations are attributed to virus invasion into the brain or just comorbidities caused by dysregulation of systemic factors. Here, we briefly review the neurological manifestations of SARS-CoV-2, summarize recent evidence for the potential neurotropism of SARS-CoV-2, and discuss the potential mechanisms of COVID-19-associated neurological diseases.