On 11 March 2020, coronavirus disease 2019 (COVID-19) was declared a pandemic by the World Health Organization (WHO). This study focuses on a narrative review about the illness during the first year of the pandemic in relation to obesity. Databases were used to search studies published up to 8 December 2020. In total, 4430 articles and other scientific literature were found, and 24 articles were included in this one-year narrative review. The mean BMI value of severe COVID-19 patients ranged from 24.5 to 33.4 kg/m2, versus <18.5 to 24.3 kg/m2 for non-severe patients. Articles using the terms obesity or overweight without indicating the BMI value in these patients were common, but this is not useful, as the anthropometric parameters, when not defined by this index, are confusing due to the classification being different in the West compared to among Asian and Korean criteria-based adults. We proposed a new term, called COVID obesity, to define the importance of this anthropometric parameter, among others, in relation with this pandemic.