This work examines the performance of Exponential-Gamma distribution and the existing Exponetial and Gamma in relative to the distribution that will best fit the data on Covid-19 death in Nigeria from March 2020 to April 2021. The parameters of the distribution were estimated using the method of maximum likelihood estimates. The newly developed Exponential-Gamma distribution was compared with the exiting Exponential and Gamma distributions using the log-likelihood function, Akaike information criterion (AIC), and Bayesian information criterion (BIC) as the criteria for selecting the best fit model. The results show that the newly developed Exponential-Gamma distribution performed better than the existing Exponential and Gamma distributions in contrast in terms of model fit, this showed that the newly developed Exponential-Gamma distribution is more flexible and precise in analyzing the Covid-19 data other than the existing Exponential and Gamma distributions.