Under-5 mortality is risk of a child dying before completing five years of age. The purpose of this study was to identify factors that affect under-five mortality based on 2016 EDHS data set using count regression model with specific objectives: to examine socio economic and demographic factors in terms of under-five death and to identify the appropriate count regression model to fit under-five death data. The survey collected information from a total of 15,683 women aged 15-49 years out of which 11951 women are considered in this study. The data were found to have excess zeros (62.5%) and the variance was higher than its mean. Thus several count models such as Poisson, NB, ZIP, ZINB, HP and HNB models were fitted to select the best model which fits the data. Among these models HNB was more appropriate to fit the data according to model selection criteria. Based on HNB model result the truncated negative binomial part, the explanatory variables like region, mother’s education level, contraceptive use, birth order, breastfeeding and birth type are statistically significant factors while for logistic part, using breastfeeding method, place of residence, region, mother’s occupation, mother’s educational level, contraceptive use, wealth index, birth type and birth order are statistically significant factor on the number of under-five death per mother in Ethiopia. Hence, the concerned body should work closely with both the private sector and civil society to teach households to have sufficient knowledge and awareness on under five mortality and mechanisms of reduction and moreover to make children very well.