The recent outbreak of the novel coronavirus, SARS-CoV-2, has emerged to be highly pathogenic in nature. Although lungs are considered as the primary infected organs by SARS-CoV-2, some of the other organs, including the brain, have also been found to be affected. Here, we have discussed how SARS-CoV-2 might infect the brain. The infection of the respiratory center in the brainstem could be hypothesized to be responsible for the respiratory failure in many COVID-19 patients. The virus might gain entry through the olfactory bulb and invade various parts of the brain, including the brainstem. Alternatively, the entry might also occur from peripheral circulation into the central nervous system by compromising the blood-brain barrier. Finally, yet another possible entry route could be its dispersal from the lungs into the vagus nerve via the pulmonary stretch receptors, eventually reaching the brainstem. Therefore, screening neurological symptoms in COVID-19 patients, especially toward the breakdown of the respiratory center in the brainstem, might help us better understand this disease.