The COVID-19 pandemic has posed a serious threat to the lives of many people across the globe. In Nigeria, the first COVID-19 case was reported on 27th February, 2020, after an Italian citizen tested positive for Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), the causative agent of COVID-19. The spread of SARS-CoV-2 remained stable until 21st April, 2020, where the number of infections in three digits emerged and as of June 20th 2020, Nigeria has a total of 19,808 confirmed cases, total discharged 6,718 and 506 deaths recorded. The severity of SARS-CoV-2 by far surpasses the coronaviruses that were so far discovered in 2003 and 2012. In this study, a Susceptible Infectious and Recovered (SIR) model for severity of COVID-19 pandemic in Nigeria has been developed to obtain the overall picture of the severity of the disease in Nigeria. Based on the simulation of the fitted model, we arrived at a basic reproductive number (R0) 1.533931 and an infected individual required 9 days to recover from the disease. The findings indicated that the fitted model satisfactorily mimicked the actual data reported by the Nigeria Center for Disease Control (NCDC). The R0 obtained showed that on the average one infected individual would spread the COVID-19 to two susceptible individuals. Though the pandemic is under control, but the government needs to take measures to totally contain the spread of the virus.