Since December 2019, every aspect of daily life has been profoundly impacted by the COVID-19 pandemic. The coronavirus spread over 200 countries worldwide and killed more than 5 million individuals. Modeling the death rate due to COVID-19 has become vital in guiding health authorities in implementing effective policies and decision-making. This research investigates the New Flexible Exponential Type Family (FETF) of distributions and explores a specific distribution within this family, the Exponential Type Weibull distribution (ETW) that can be used to model the mortality rate COVID-19 patients. The research thoroughly explores ETW characteristics, such as order statistics, moments, survival function, hazard function, mean residual life function, and quantile function. The widely accepted likelihood approach is employed to estimate the unknown parameters in the suggested model. The recommended model is carefully tested against real-world non-monotonic COVID-19 data and simulated datasets to determine its usefulness.  The results exhibit the superior performance of the recommended model when compared to several prominent alternatives.