Abstract: Motivated by the case fatality rate (CFR) of COVID-19, in this paper, we develop a fully parametric quantile regression model based on the generalized three-parameter beta (GB3) distribution. Generally, beta regression models are primarily used to deal with data arising from rates and proportions. However, these models are usually specified in terms of a conditional mean. Therefore, they may be inadequate if the observed response variable follows an asymmetrical distribution, such as CFR data. In addition, beta regression models do not take into account the effect of the covariates across the spectrum of the dependent variable, which is possible through conditional quantile approach. In order to introduce the proposed GB3 regression model, we introduce a reparameterization of this distribution by inserting a quantile parameter, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we proposed a simple interpretation of the predictor-response relationships in terms of percentage increases/decreases of the quantile. A Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates and the choice of the link functions. A real COVID-19 data set is finally analyzed to illustrate the proposed approach.