Poisson regression model is widely used in software quality modeling. When the response variable of a data set includes a large number of zeros, Poisson regression model will underestimate the probability of zeros. A zero-inflated model changes the mean structure of the pure Poisson model. The predictive quality is therefore improved. In this paper, we examine a full-scale in-dustrial software system and develop two models, Poisson regression and zero-inflated Poisson regression. To our knowledge, this is the first study that introduces the zero-inflated Poisson regression model in software reliability. Comparing the predictivequalities of the two competing models, we conclude that for this system, the zero-inflated Poisson regression model is more appropriate in theory and practice.