Neural network based deep learning techniques have shown great success for numerous applications. While it is expected to understand their intrinsic decision-making processes, these deep neural networks often work in a black-box way. To this end, in this paper, we aim to discern the decision-making processes of neural networks through a hierarchical voting strategy by developing an explainable deep learning model, namely Voting Transformation-based Explainable Neural Network (VOTEN). Specifically, instead of relying on massive feature combinations, VOTEN creatively models expressive single-valued voting functions between explicitly modeled latent concepts to achieve high fitting ability. Along this line, we first theoretically analyze the major components of VOTEN and prove the relationship and advantages of VOTEN compared with Multi-Layer Perceptron (MLP), the basic structure of deep neural networks. Moreover, we design efficient algorithms to improve the model usability by explicitly showing the decision processes of VOTEN. Finally, extensive experiments on multiple real-world datasets clearly validate the performances and explainability of VOTEN.