Lack assumption that commonly happens in Poisson model is over-dispersion. Over-dispersion is a condition in which the variance value is larger than mean of response variable. The aim of this research is to analyze Poisson models, i.e. Poisson Regression (POI), Zero-Inflated Poisson Regression (ZIP), Generalized Poisson Regression (GP) and Zero-Inflated Generalized Poisson Regression (ZIGP) of over-dispersion data. The data used in this research is Indonesian Demographic and Health Survey (SKDI) Data in 2017. Total number of 17.212 families with response variable of child mortality in these families become the objects of the study. The estimator of parameter model is Maximum likelihood estimator (MLE). The results analysis of those four models aforementioned above show that over-dispersion case causes the usage of POI model becomes less appropriate, while GP model can be used for over-dispersion case, however if the case of over-dispersion is caused by zero excess in the data, GP will be better than ZIP and ZIGP. It can be seen in the minimum of AIC value reached by each model through the data of SDKI with zero excess (having >50% of zero numbers), in which POI =13922, GP = 13578, ZIP = 13589 and ZIGP = 13588. Thus, it can be concluded that in over-dispersion data with zero excess (with big numbers of zero), ZIGP is less appropriate to be applied, because range of data is short (0-6).