Let ℤ _{p² } ⋊ _{ϕ } ℤ _{p } be the semi-direct product of ℤ _{p² } and ℤ _{p } with respect to ϕ, (ϕ is homomorphism from ℤ _{p } to automorphisms group of ℤ _{p² }). In this work, the group Aut _{C }( ℤ _{3² } ⋊ _{ϕ } ℤ₃ ) of all central automorphisms of ℤ _{3² } ⋊ _{ϕ } ℤ₃ is studied and we determine the form of central automorphisms of ℤ _{3² } ⋊ _{ϕ } ℤ _{3 } .