Channel pruning is a promising method for accelerating and compressing convolutional neural networks. However, current pruning algorithms still remain unsolved problems that how to assign layer-wise pruning ratios properly and discard the least important channels with a convincing criterion. In this paper, we present a novel channel pruning approach via information theory and interpretability of neural networks. Specifically, we regard information entropy as the expected amount of information for convolutional layers. In addition, if we suppose a matrix as a system of linear equations, a higher-rank matrix represents there exist more solutions to it, which indicates more uncertainty. From the point of view of information theory, the rank can also describe the amount of information. In a neural network, considering the rank and entropy as two information indicators of convolutional layers, we propose a fusion function to reach a compromise of them, where the fusion results are defined as ``information concentration''. When pre-defining layer-wise pruning ratios, we employ the information concentration as a reference instead of heuristic and engineering tuning to provide a more interpretable solution. Moreover, we leverage Shapley values, which are a potent tool in the interpretability of neural networks, to evaluate the channel contributions and discard the least important channels for model compression while maintaining its performance. Extensive experiments demonstrate the effectiveness and promising performance of our method. For example, our method improves the accuracy by 0.21% when reducing 45.5% FLOPs and removing 40.3% parameters for ResNet-56 on CIFAR-10. Moreover, our method obtains loss in Top-1/Top-5 accuracies of 0.43%/0.11% by reducing 41.6% FLOPs and removing 35.0% parameters for ResNet-50 on ImageNet.