This paper discusses the hierarchies of some classes of recursive functions. A simple equivalent definition of original Grzegorczyk's hierarchy is presented at first. Then the authors define by the generalization of Ackermann's function a sequence of recursive functions {A_ｎ｝_ｎ∈ω, based on which they define hierarchy, {Z_ｎ｝_ｎ∈ω(the Z-hierarchy)of a class of recursive functions which is much larger than the class of primitive recursive functions.The first level Z_０ of this hierarchy is just the class of primitive recursive functions.For all n, Z_n+1 contains the universal function of its predecessor Z_n. A refinement {Z_ｎⁱ｝_ｎ,i∈ωof Z-hierarchy is defined at last by the natural hierarchy of each Z_n. The refinement on Z_O is same as the original Grzegorczyk's hierarchy. This shows that their Z-hierarchy and its refinement are really a natural extension of Grzegorczyk's hierarchy.