Summary: The cycle-structure of hypergraph plays an important role in the hypergraph theory and the database theory. It has been well studied during last several years. Especially in recent years, many researchers continue to study. J. F. Wang [Acta Math. Appl. Sin., Engl. Ser. 21, No. 3, 495–498 (2005; Zbl 1103.05057)] introduced the cycle-axiom of hypergraph. In this paper, we make a note of cycle-axiom of hypergraph to explain that the cycle-axiom of hypergraph is reasonable, and displays an important role in the hypergraph theory.