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In computer vision, some attribution methods for explaining CNNs attempt to study how the intermediate features affect the network prediction. However, they usually ignore the feature hierarchies among the intermediate features. This paper introduces a hierarchical decomposition framework to explain CNN's decision-making process in a top-down manner. Specifically, we propose a gradient-based activation propagation (gAP) module that can decompose any intermediate CNN decision to its lower layers and find the supporting features. Then we utilize the gAP module to iteratively decompose the network decision to the supporting evidence from different CNN layers. The proposed framework can generate a deep hierarchy of strongly associated supporting evidence for the network decision, which provides insight into the decision-making process. Moreover, gAP is effort-free for understanding CNN-based models without network architecture modification and extra training process. Experiments show the effectiveness of the proposed method. The code and interactive demo website will be made publicly available.