A Poisson model typically is assumed for count data, but when there are so many zeroes in the response variable, because of overdispersion, a negative binomial regression is suggested as a count regression instead of Poisson regression. In this paper, a zero-inflated negative binomial regression model with right truncation count data was developed. In this model, we considered a response variable and one or more than one explanatory variables. The estimation of regression
parameters using the maximum likelihood method was discussed and the goodness-of-fit for the regression model was examined. We studied the effects of truncation in terms of parameters estimation, their standard errors and the goodnessof-fit statistics via real data. The results showed a better fit by using a truncated zero-inflated negative binomial regression model when the response variable has many zeros and it was right truncated.