Objectives: The potential burden of COVID-19 in sub-Saharan African might be substantially more significant than reported, and more than the existing health system can handle. Hence, in this study, we estimate and project the burden and transmission risk of COVID-19, in Nigeria, using current interventions. Methods: Modified SEIR epidemic mathematical model was used to simulate the disease progression in weeks, for up to 19 weeks. Different situations, involving zero-intervention and varying degrees of interventions are modeled. For the intervention phase, 25% and 75% social distancing are considered, while border closure includes 80% closure of airports, seaports, and intra-state borders, using available data as of 15th May 2020. Results: The effects of various interventions on the R0 of COVID-19 are presented. A higher percentage of social distancing appears to be more effective in controlling the spread of COVID-19 in Nigeria than border closure. Up to 131,000 persons could be infected if there are no interventions. Conclusion: According to our results, it is easier to enforce 75% closures than 25%, as the percentage of the population complying with social distancing is higher when at least 75% of public places were closed. The minimum requirement of the population percentage that needs to comply with the social distancing advice, to weaken the epidemic can be obtained from the model.