This paper aims to quantitatively explain the rationales of each prediction that is made by a pre-trained convolutional neural network (CNN). We propose to learn a decision tree, which clarifies the specific reason for each prediction made by the CNN at the semantic level. Ie, the decision tree decomposes feature representations in high conv-layers of the CNN into elementary concepts of object parts. In this way, the decision tree tells people which object parts activate which filters for the prediction and how much each object part contributes to the prediction score. Such semantic and quantitative explanations for CNN predictions have specific values beyond the traditional pixel-level analysis of CNNs. More specifically, our method mines all potential decision modes of the CNN, where each mode represents a typical case of how the CNN uses object parts for prediction. The decision tree organizes all potential decision modes in a coarse-to-fine manner to explain CNN predictions at different fine-grained levels. Experiments have demonstrated the effectiveness of the proposed method.