Summary: We propose a new regression tree algorithm called CounTree for analysis of a dataset with count response. CounTree includes powerful node models and a restricted splitting rule and stopping rule. CounTree focuses on handling the exceptions to the Poisson distribution assumption to improve the regression model's accuracy and the tree-based method's interpretability. It allows both overdispersion and inflation of zeros in the Poisson distribution. Besides, it also provides optional variable selection and regularization in the regression model, which can improve the estimation of coefficients when there are many noise variables, collinearity or categorical covariates with too many levels. CounTree inherits the advantages of tree methods: (1). it handles stratified data, (2). it detects interactions, (3). it produces easy to interpret results with visualization and (4). it requires minimal data preparation. Moreover, it also has plenty of options for node models. Simulation studies and real dataset examples show that CounTree has better interpretability and prediction accuracy compared to other tree-based methods and ensemble methods.