A Poisson model typically is assumed for count data. It is assumed to have the same value for expectation and variance in a Poisson distribution, but most of the time there is over-dispersion in the model. Furthermore, the response variable in such cases is truncated for some outliers or large values. In this paper, a Poisson regression model is introduced on truncated data. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness-of-fit for the regression model is examined. We study the effects of truncation in terms of parameters estimation and their standard errors via real data.