With the great success of networks, it witnesses the increasing demand for the interpretation of the internal network mechanism, especially for the net decision-making logic. To tackle the challenge, the Concept-harmonized HierArchical INference (CHAIN) is proposed to interpret the net decision-making process. For net-decisions being interpreted, the proposed method presents the CHAIN interpretation in which the net decision can be hierarchically deduced into visual concepts from high to low semantic levels. To achieve it, we propose three models sequentially, i.e., the concept harmonizing model, the hierarchical inference model, and the concept-harmonized hierarchical inference model. Firstly, in the concept harmonizing model, visual concepts from high to low semantic-levels are aligned with net-units from deep to shallow layers. Secondly, in the hierarchical inference model, the concept in a deep layer is disassembled into units in shallow layers. Finally, in the concept-harmonized hierarchical inference model, a deep-layer concept is inferred from its shallow-layer concepts. After several rounds, the concept-harmonized hierarchical inference is conducted backward from the highest semantic level to the lowest semantic level. Finally, net decision-making is explained as a form of concept-harmonized hierarchical inference, which is comparable to human decision-making. Meanwhile, the net layer structure for feature learning can be explained based on the hierarchical visual concepts. In quantitative and qualitative experiments, we demonstrate the effectiveness of CHAIN at the instance and class levels.