Abstract: The concept of Fuzzy sets was first introduced by L.A.Zadeh in 1965 and Fuzzy integral was set up by M.Sugeno in 1972.Later, a series of distribution function convergence theorems and Fuzzy integral measure convergence theorems were established by Huang Jin-Li and Zheng Dao-Peng in 1980. In the same year, the Fuzzy integral set up by M.Sugeno (it is called Fuzzy integral of type I in this paper) was extended and a new Fuzzy integral (this is named Fuzzy integral type I in this paper) was introduced by Zhang Wen-xiu and Zhao Ru-huai Starting with Fuzzy integral of type I, this paper presents the corresponding convergence theorem of Fuzzy integral of type I.