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Convolutional neural network (CNN) models have seen advanced improvements in performance in various domains, but lack of interpretability is a major barrier to assurance and regulation during operation for acceptance and deployment of AI-assisted applications. There have been many works on input interpretability focusing on analyzing the input-output relations, but the internal logic of models has not been clarified in the current mainstream interpretability methods. In this study, we propose a novel hybrid CNN-interpreter through: (1) An original forward propagation mechanism to examine the layer-specific prediction results for local interpretability. (2) A new global interpretability that indicates the feature correlation and filter importance effects. By combining the local and global interpretabilities, hybrid CNN-interpreter enables us to have a solid understanding and monitoring of model context during the whole learning process with detailed and consistent representations. Finally, the proposed interpretabilities have been demonstrated to adapt to various CNN-based model structures.