In this study, we propose a new zero-inflated regression model as an alternative to zero-inflated regression models, such as the zero-inflated Poisson, zero-inflated negative binomial, zero-inflated hurdle-Poisson, and zero-inflated hurdle negative binomial models. In this regard, we take benefit of the flexibility of the Poisson–Bilal distribution and some of its notable properties. More concretely, it is employed as the baseline distribution to generate a new regression model called the zero-inflated Poisson-Bilal regression model. It is designed to be a good alternative for modeling overdispersed data quite effectively. This aspect is emphasized using two real-world data sets from the medicine and education fields. Furthermore, these data sets are analyzed to compare the goodness-of-fit of the suggested zero-inflated regression model with some of its direct competitors.