Case fatality rate, an indicator of disease severity, is one of the most important parameters in medical and epidemiological studies. Simple naive estimate method is often used to estimate case fatality rate. However, the naive method can lead to biased estimates for a number of reasons including, for example, ascertainment error and incomplete data. Here, we developed a new model called NELM (derived from Naive Estimate and Linear Model), which incorporates both the naive method and the regression models, for the regression model takes Gaussian random error into account. We illustrated the algorithm using Ebola epidemic data of three West African countries. Our algorithm is robust and effective. And it provides insight into the ongoing Ebola outbreak and other emerging infectious diseases.