Motivation: Computational prediction of multiple-type drug-drug interaction (DDI) helps reduce unexpected side effects in poly-drug treatments. Although existing computational approaches achieve inspiring results, they ignore that the action of a drug is mainly caused by its chemical substructures. In addition, their interpretability is still weak. Results: In this paper, by supposing that the interactions between two given drugs are caused by their local chemical structures (sub-structures) and their DDI types are determined by the linkages between different substructure sets, we design a novel Substructure-ware Tensor Neural Network model for DDI prediction (STNN-DDI). The proposed model learns a 3-D tensor of (substructure, in-teraction type, substructure) triplets, which characterizes a substructure-substructure interaction (SSI) space. According to a list of predefined substructures with specific chemical meanings, the mapping of drugs into this SSI space enables STNN-DDI to perform the multiple-type DDI prediction in both transductive and inductive scenarios in a unified form with an explicable manner. The compar-ison with deep learning-based state-of-the-art baselines demonstrates the superiority of STNN-DDI with the significant improvement of AUC, AUPR, Accuracy, and Precision. More importantly, case studies illustrate its interpretability by both revealing a crucial sub-structure pair across drugs regarding a DDI type of interest and uncovering interaction type-specific substructure pairs in a given DDI. In summary, STNN-DDI provides an effective approach to predicting DDIs as well as explaining the interaction mechanisms among drugs.