A Poisson model typically is assumed for count data. In many cases because of many zeros in the response variable, the mean is not equal to the variance value of the dependent variable. Therefore, the Poisson model is no longer suitable for this kind of data. Thus, we suggest using a hurdle negative binomial regression model to overcome the problem of overdispersion. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle negative binomial regression model is introduced on count data with many zeros. The estimation of regression parameters using maximum likelihood is discussed and the goodness-of-fit for the regression model is examined