The CTR (Click-Through Rate) prediction plays a central role in the domain of computational advertising and recommender systems. There exists several kinds of methods proposed in this field, such as Logistic Regression (LR), Factorization Machines (FM) and deep learning based methods like Wide&Deep, Neural Factorization Machines (NFM) and DeepFM. However, such approaches generally use the vector-product of each pair of features, which have ignored the different semantic spaces of the feature interactions. In this paper, we propose a novel Tensor-based Feature interaction Network (TFNet) model, which introduces an operating tensor to elaborate feature interactions via multi-slice matrices in multiple semantic spaces. Extensive offline and online experiments show that TFNet: 1) outperforms the competitive compared methods on the typical Criteo and Avazu datasets; 2) achieves large improvement of revenue and click rate in online A/B tests in the largest Chinese App recommender system, Tencent MyApp.