The excess of zeros is not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM of Cantoni and Ronchetti (2001) to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions.