The Coronavirus Disease 2019 (COVID-19) has posed a great threat to global public health; of which was reported to emerge in Wuhan, China at the end of the year 2019. It became alarming to Nigerians when Nigeria recorded her first index case in February 2020 in the city of Lagos which has led to a total number of 5162 confirmed cases, 1180 recovered with 167 death recorded as at May 14, 2020. This paper proposes a mathematical model SEIQCRW which adopt the SEIR model to study the current outbreak of COVID-19 in Nigeria with nonlinear forces of infection. This model defines the transmission channels in the infection dynamics and the impact of the environmental reservoir in the transmission and spread of this disease to humans. The existence of the region where the model is epidemiologically feasible is established. A detailed numerical simulation of this model was conducted using the Nigeria Centre for Disease Control (NCDC) reported data. Our analytical and simulation results between February 29, 2020 and May 14, 2020 are in good agreement. Further simulation indicates that Nigeria's cumulative number of confirmed cases will reach 55,000 individuals in December 25, 2020. Mitigation strategies and its effectiveness in reducing the spread of COVID-19 across Nigeria are considered.