3D convolution is powerful for video classification but often computationally expensive, recent studies mainly focus on decomposing it on spatial-temporal and/or channel dimensions. Unfortunately, most approaches fail to achieve a preferable balance between convolutional efficiency and feature-interaction sufficiency. For this reason, we propose a concise and novel Channel Tensorization Network (CT-Net), by treating the channel dimension of input feature as a multiplication of K sub-dimensions. On one hand, it naturally factorizes convolution in a multiple dimension way, leading to a light computation burden. On the other hand, it can effectively enhance feature interaction from different channels, and progressively enlarge the 3D receptive field of such interaction to boost classification accuracy. Furthermore, we equip our CT-Module with a Tensor Excitation (TE) mechanism. It can learn to exploit spatial, temporal and channel attention in a high-dimensional manner, to improve the cooperative power of all the feature dimensions in our CT-Module. Finally, we flexibly adapt ResNet as our CT-Net. Extensive experiments are conducted on several challenging video benchmarks, e.g., Kinetics-400, Something-Something V1 and V2. Our CT-Net outperforms a number of recent SOTA approaches, in terms of accuracy and/or efficiency.