Coronavirus disease 2019 (COVID-19), a disease caused by the novel betacoronavirus (SARS-CoV-2), has become a global pandemic threat. The potential involvement of COVID-19 in central nervous system (CNS) has attracted considerable attention due to neurological manifestations presented throughout the disease process. In addition, SARS-CoV-2 is structurally similar to SARS-CoV, and both bind to the angiotensin-converting enzyme 2 (ACE2) receptor to enter human cells. Thus, cells expressing ACE2, such as neurons and glial cells may act as targets and are thus vulnerable to SARS-CoV-2 infection. Here, we have reviewed the neurological characteristics of COVID-19 and summarized possible mechanisms of SARS-CoV-2 invasion of the CNS. COVID-19 patients have presented with a number of different neurological symptoms such as headache, dizziness, hyposmia, and hypogeusia during the course of illness. It has also been reported recently that some cases of COVID-19 have presented with concurrent acute cerebrovascular disease (acute ischemic stroke, cerebral venous sinus thrombosis, cerebral hemorrhage, subarachnoid hemorrhage), meningitis/encephalitis, acute necrotizing hemorrhagic encephalopathy, and acute Guillain-Barre syndrome. Furthermore, SARS-CoV-2 RNA detected in a cerebrospinal fluid specimen of a patient with COVID-19 have provided direct evidence to support the theory of neurotropic involvement of SARS-CoV-2. However, the underlying neurotropic mechanisms of SARS-CoV-2 are yet to be established. SARS-CoV-2 may affect CNS through two direct mechanisms (hematogenous dissemination or neuronal retrograde dissemination) or via indirect routes. The underlying mechanisms require further elucidation in the future.