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Class activation map (CAM) has been widely studied for visual explanation of the internal working mechanism of convolutional neural networks. The key of existing CAM-based methods is to compute effective weights to combine activation maps in the target convolution layer. Existing gradient and score based weighting schemes have shown superiority in ensuring either the discriminability or faithfulness of the CAM, but they normally cannot excel in both properties. In this paper, we propose a novel CAM weighting scheme, named FD-CAM, to improve both the faithfulness and discriminability of the CAM-based CNN visual explanation. First, we improve the faithfulness and discriminability of the score-based weights by performing a grouped channel switching operation. Specifically, for each channel, we compute its similarity group and switch the group of channels on or off simultaneously to compute changes in the class prediction score as the weights. Then, we combine the improved score-based weights with the conventional gradient-based weights so that the discriminability of the final CAM can be further improved. We perform extensive comparisons with the state-of-the-art CAM algorithms. The quantitative and qualitative results show our FD-CAM can produce more faithful and more discriminative visual explanations of the CNNs. We also conduct experiments to verify the effectiveness of the proposed grouped channel switching and weight combination scheme on improving the results. Our code is available at https://github.com/crishhh1998/FD-CAM.